Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
25801	Check if Differentiable Over an Interval	y=100-x^2 , [-10,10]	$y = 100 - x^{2}$ , $[- 10, 10]$
25802	Check if Differentiable Over an Interval	y=25-x^2 , [-5,5]	$y = 25 - x^{2}$ , $[- 5, 5]$
25803	Evaluate the Integral	integral from 0.25 to 0.5 of 1/( square root of 25-16x^2) with respect to x	$\int_{0.25}^{0.5} \frac{1}{\sqrt{25 - 16 x^{2}}} d x$
25804	Evaluate the Integral	integral from 0.4 to 1 of x^4cot(x^5) with respect to x	$\int_{0.4}^{1} x^{4} \cot (x^{5}) d x$
25805	Find the Derivative - d/dx	2^90	$2^{90}$
25806	Evaluate the Integral	integral of 0.03x with respect to x	$\int 0.03 x d x$
25807	Find the Derivative - d/dx	2/( cube root of x)+3cos(x)	$\frac{2}{\sqrt[3]{x}} + 3 \cos (x)$
25808	Evaluate the Integral	integral from 0 to pi of (e^(cos(t)))(sin(2t)) with respect to t	$\int_{0}^{π} (e^{\cos (t)}) (\sin (2 t)) d t$
25809	Evaluate the Integral	integral from 0 to pi of (sin(4x)^6)cos(4x) with respect to x	$\int_{0}^{π} (\sin^{6} (4 x)) \cos (4 x) d x$
25810	Evaluate the Integral	integral from 0 to 8 of xe^(-x/c) with respect to x	$\int_{0}^{8} x e^{- \frac{x}{c}} d x$
25811	Evaluate the Integral	integral from 0 to 9 of 1/( square root of x) with respect to x	$\int_{0}^{9} \frac{1}{\sqrt{x}} d x$
25812	Evaluate the Integral	integral from 0 to pi of tan(x/3)^2 with respect to x	$\int_{0}^{π} \tan^{2} (\frac{x}{3}) d x$
25813	Evaluate the Integral	integral from 0 to pi of 2sin(x)+sin(2x) with respect to x	$\int_{0}^{π} 2 \sin (x) + \sin (2 x) d x$
25814	Find the Derivative - d/dx	x^7(5+8x)^3	$x^{7} {(5 + 8 x)}^{3}$
25815	Evaluate the Integral	integral from 0 to 7 of 4x* cube root of x+1 with respect to x	$\int_{0}^{7} 4 x \cdot \sqrt[3]{x + 1} d x$
25816	Solve for x	natural log of x^2=10	$\ln (x^{2}) = 10$
25817	Solve for x	e^(2-4x)=9	$e^{2 - 4 x} = 9$
25818	Solve for x	2^(2x)-3.2^x+2=0	$2^{2 x} - {3.2}^{x} + 2 = 0$
25819	Evaluate the Integral	integral from 0 to 2 of 3e^x with respect to x	$\int_{0}^{2} 3 e^{x} d x$
25820	Evaluate the Integral	integral from 0 to 2 of 2f(x) with respect to x	$\int_{0}^{2} 2 f (x) d x$
25821	Find the Derivative - d/dx	y=8cos(4x)	$y = 8 \cos (4 x)$
25822	Evaluate the Integral	integral from 0 to 1 of -5x with respect to x	$\int_{0}^{1} - 5 x d x$
25823	Find dy/dx	y=7/( square root of x)	$y = \frac{7}{\sqrt{x}}$
25824	Evaluate the Integral	integral from 0 to 1 of 6 sixth root of x with respect to x	$\int_{0}^{1} 6 \sqrt[6]{x} d x$
25825	Evaluate the Integral	integral from 0 to 1 of 3cos((pit)/2) with respect to t	$\int_{0}^{1} 3 \cos (\frac{π t}{2}) d t$
25826	Find dy/dx	y=x^2-3x	$y = x^{2} - 3 x$
25827	Find dy/dx	y=-y/x	$y = - \frac{y}{x}$
25828	Evaluate the Integral	integral from 0 to 1 of x^3(2x^4+3)^2 with respect to x	$\int_{0}^{1} x^{3} {(2 x^{4} + 3)}^{2} d x$
25829	Evaluate the Integral	integral from 0 to 10 of x^2( square root of x+7)^2 with respect to x	$\int_{0}^{10} x^{2} {(\sqrt{x} + 7)}^{2} d x$
25830	Evaluate the Integral	integral from 0 to 10 of -0.006t^2+0.2t with respect to x	$\int_{0}^{10} - 0.006 t^{2} + 0.2 t d x$
25831	Evaluate the Integral	integral from 0 to 10 of 2000e^(0.3t) with respect to t	$\int_{0}^{10} 2000 e^{0.3 t} d t$
25832	Evaluate the Integral	integral from 0 to 10 of (24t)/(2t+3) with respect to t	$\int_{0}^{10} \frac{24 t}{2 t + 3} d t$
25833	Evaluate the Integral	integral from 0 to 120 of 10+ square root of t with respect to t	$\int_{0}^{120} 10 + \sqrt{t} d t$
25834	Evaluate the Integral	integral of 12 cube root of cos(x)sin(x) with respect to x	$\int 12 \sqrt[3]{\cos (x)} \sin (x) d x$
25835	Find the Local Maxima and Minima	f(x)=64x^3-12x+1	$f (x) = 64 x^{3} - 12 x + 1$
25836	Evaluate the Integral	integral of 14(x-5)^6 with respect to x	$\int 14 {(x - 5)}^{6} d x$
25837	Evaluate the Integral	integral from 140 to 200 of 1/(15 square root of 2p)*e^(-((x-100)^2)/450) with respect to x	$\int_{140}^{200} \frac{1}{15 \sqrt{2 p}} \cdot e^{- \frac{{(x - 100)}^{2}}{450}} d x$
25838	Find the Antiderivative	e^(6x)	$e^{6 x}$
25839	Find the Difference Quotient	f(x)=-3x^2-4x-2	$f (x) = - 3 x^{2} - 4 x - 2$
25840	Evaluate the Integral	integral from 10 to 20 of 30/x+25 with respect to x	$\int_{10}^{20} \frac{30}{x} + 25 d x$
25841	Evaluate the Integral	integral of 10 cube root of x^2 with respect to x	$\int 10 \sqrt[3]{x^{2}} d x$
25842	Evaluate the Limit	limit as x approaches 17 of (x-17)/(x^2-289)	$lim_{x \to 17} \frac{x - 17}{x^{2} - 289}$
25843	Evaluate the Integral	integral from 1 to e of 7/x with respect to x	$\int_{1}^{e} \frac{7}{x} d x$
25844	Evaluate the Limit	limit as x approaches 2 of (sin(x-3))/(x^2-9)	$lim_{x \to 2} \frac{\sin (x - 3)}{x^{2} - 9}$
25845	Evaluate the Integral	integral from 1 to e of natural log of 5x with respect to x	$\int_{1}^{e} \ln (5 x) d x$
25846	Evaluate the Limit	limit as x approaches -6 of f(x)	$lim_{x \to - 6} f (x)$
25847	Evaluate the Limit	limit as x approaches 1 of x^(1/(1-x))	$lim_{x \to 1} x^{\frac{1}{1 - x}}$
25848	Evaluate the Integral	integral from 1 to e of (4x^3-3x)/(x^2) with respect to x	$\int_{1}^{e} \frac{4 x^{3} - 3 x}{x^{2}} d x$
25849	Evaluate the Integral	integral from 1 to e of (x^2-1)/x with respect to x	$\int_{1}^{e} \frac{x^{2} - 1}{x} d x$
25850	Evaluate the Integral	integral of 1-csc(2x)^2 with respect to x	$\int 1 - \csc^{2} (2 x) d x$
25851	Evaluate the Integral	integral from 1 to pi of e^(cos(x))sin(2x) with respect to x	$\int_{1}^{π} e^{\cos (x)} \sin (2 x) d x$
25852	Evaluate the Integral	integral from 1 to -5 of 2x-3 with respect to x	$\int_{1}^{- 5} 2 x - 3 d x$
25853	Evaluate the Integral	integral from 1 to 7 of natural log of 20x with respect to x	$\int_{1}^{7} \ln (20 x) d x$
25854	Evaluate the Integral	integral from 1 to 7 of x square root of 6x^2+4 with respect to x	$\int_{1}^{7} x \sqrt{6 x^{2} + 4} d x$
25855	Evaluate the Integral	integral of ( natural log of x)/(x^3) with respect to x	$\int \frac{\ln (x)}{x^{3}} d x$
25856	Evaluate the Integral	integral of \|x\| with respect to x	$\int \| x \| d x$
25857	Evaluate the Integral	integral of square root of 9x^4-6x^2+1 with respect to x	$\int \sqrt{9 x^{4} - 6 x^{2} + 1} d x$
25858	Evaluate the Integral	integral from 0 to 6 of square root of 36-x^2 with respect to x	$\int_{0}^{6} \sqrt{36 - x^{2}} d x$
25859	Evaluate the Integral	integral from -1 to 3 of 4-5x with respect to x	$\int_{- 1}^{3} 4 - 5 x d x$
25860	Evaluate the Integral	integral from 1 to 3 of (6x^2)/(8x^3+1) with respect to x	$\int_{1}^{3} \frac{6 x^{2}}{8 x^{3} + 1} d x$
25861	Evaluate the Integral	integral of 1/((16-x^2)^(3/2)) with respect to x	$\int \frac{1}{{(16 - x^{2})}^{\frac{3}{2}}} d x$
25862	Evaluate the Integral	integral from 1 to 4 of 4/x with respect to x	$\int_{1}^{4} \frac{4}{x} d x$
25863	Evaluate the Integral	integral from 1 to 32 of x^(-(7/5)) with respect to x	$\int_{1}^{32} x^{- (\frac{7}{5})} d x$
25864	Evaluate the Summation	sum from k=1 to 15 of 3k+10	$\sum_{k = 1}^{15} 3 k + 10$
25865	Evaluate the Integral	integral from 1 to 3 of -3/x with respect to x	$\int_{1}^{3} - \frac{3}{x} d x$
25866	Evaluate the Integral	integral of 18x^17 with respect to x	$\int 18 x^{17} d x$
25867	Evaluate the Integral	integral of 14x natural log of 5x with respect to x	$\int 14 x \ln (5 x) d x$
25868	Evaluate the Integral	integral of -15x^4(-3x^5-1)^5 with respect to x	$\int - 15 x^{4} {(- 3 x^{5} - 1)}^{5} d x$
25869	Evaluate the Summation	sum from k=15 to 18 of (-1)^k(3k)	$\sum_{k = 15}^{18} {(- 1)}^{k} (3 k)$
25870	Evaluate the Summation	sum from k=3 to 6 of 9k-2	$\sum_{k = 3}^{6} 9 k - 2$
25871	Evaluate the Summation	sum from n=1 to infinity of 12(-1/9)^(n-1)	$\sum_{n = 1}^{\infty} 12 {(- \frac{1}{9})}^{n - 1}$
25872	Evaluate the Integral	integral from -2 to 4 of 2+1/2y-1/4y^2 with respect to y	$\int_{- 2}^{4} 2 + \frac{1}{2} y - \frac{1}{4} y^{2} d y$
25873	Find the Inverse	f(x)=2sin(x)-1	$f (x) = 2 \sin (x) - 1$
25874	Find Where Increasing/Decreasing Using Derivatives	e^(5x)+e^(-x)	$e^{5 x} + e^{- x}$
25875	Find Where Increasing/Decreasing Using Derivatives	x^(1/3)(x+4)	$x^{\frac{1}{3}} (x + 4)$
25876	Find the Concavity	f(x)=(x+3)^4	$f (x) = {(x + 3)}^{4}$
25877	Evaluate the Integral	integral from 2 to 8 of 10+3.75t with respect to t	$\int_{2}^{8} 10 + 3.75 t d t$
25878	Evaluate the Integral	integral of 200x^4 with respect to x	$\int 200 x^{4} d x$
25879	Evaluate the Integral	integral of 2y^2x-3 with respect to x	$\int 2 y^{2} x - 3 d x$
25880	Evaluate the Integral	integral from -20 to -1 of 3/(e^(-z))-1/(3z) with respect to z	$\int_{- 20}^{- 1} \frac{3}{e^{- z}} - \frac{1}{3 z} d z$
25881	Evaluate the Integral	integral from 20 to 130 of 42.07e^(-0.01059t) with respect to t	$\int_{20}^{130} 42.07 e^{- 0.01059 t} d t$
25882	Evaluate the Integral	integral of 2sec(4x)tan(4x) with respect to x	$\int 2 \sec (4 x) \tan (4 x) d x$
25883	Evaluate the Integral	integral from 2 to 5 of 355t+1125 with respect to t udu	$\int_{2}^{5} 355 t + 1125 d t$ udu
25884	Evaluate the Integral	integral of sin(x)e^x with respect to x	$\int \sin (x) e^{x} d x$
25885	Evaluate the Integral	integral of tan(x)sec(x)^4 with respect to x	$\int \tan (x) \sec^{4} (x) d x$
25886	Evaluate the Integral	integral of sin(4x)^2 with respect to x	$\int \sin^{2} (4 x) d x$
25887	Evaluate the Integral	integral of sixth root of x with respect to x	$\int \sqrt[6]{x} d x$
25888	Find the 2nd Derivative	xcos(x)	$x \cos (x)$
25889	Evaluate the Integral	integral of 6x-7 with respect to x	$\int 6 x - 7 d x$
25890	Evaluate the Integral	integral of (t square root of t+ square root of t)/(t^2) with respect to t	$\int \frac{t \sqrt{t} + \sqrt{t}}{t^{2}} d t$
25891	Evaluate the Integral	integral of t^2sin(Bt) with respect to t	$\int t^{2} \sin (B t) d t$
25892	Evaluate the Limit	limit as x approaches 3 of square root of 3-x	$lim_{x \to 3} \sqrt{3 - x}$
25893	Evaluate the Integral	integral of (tan(x))/(cos(x)^3) with respect to x	$\int \frac{\tan (x)}{\cos^{3} (x)} d x$
25894	Evaluate the Integral	integral of (t-2t^8)/( square root of t) with respect to t	$\int \frac{t - 2 t^{8}}{\sqrt{t}} d t$
25895	Evaluate the Integral	integral of square root of (a-x)/(a+x) with respect to x	$\int \sqrt{\frac{a - x}{a + x}} d x$
25896	Evaluate the Integral	integral from square root of x to 2x of arctan(t) with respect to t	$\int_{\sqrt{x}}^{2 x} \arctan (t) d t$
25897	Find dy/dx	x^2+2xy-y^2=6	$x^{2} + 2 x y - y^{2} = 6$
25898	Evaluate the Integral	integral of square root of x(6-x) with respect to x	$\int \sqrt{x} (6 - x) d x$
25899	Find the Asymptotes	f(x)=(3x^3-x^2-48x+16)/(x^2+5x+4)	$f (x) = \frac{3 x^{3} - x^{2} - 48 x + 16}{x^{2} + 5 x + 4}$
25900	Find dy/dx	y = square root of 2x-1	$y = \sqrt{2 x - 1}$