Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
38101	Find the Local Maxima and Minima	y=-x+2cos(x)	$y = - x + 2 \cos (x)$
38102	Find the Local Maxima and Minima	y=x+2sin(x)	$y = x + 2 \sin (x)$
38103	Find the Local Maxima and Minima	y=x square root of 5-x	$y = x \sqrt{5 - x}$
38104	Find the Average Value of the Function	f(x)=2x^2-3 , [1,3]	$f (x) = 2 x^{2} - 3$ , $[1, 3]$
38105	Find the Average Value of the Function	f(x)=-2x^3+21x^2-60x , [1,6]	$f (x) = - 2 x^{3} + 21 x^{2} - 60 x$ , $[1, 6]$
38106	Find the Average Value of the Function	f(x)=2x^3+3x^2 , [1,4]	$f (x) = 2 x^{3} + 3 x^{2}$ , $[1, 4]$
38107	Find the Average Value of the Function	f(x)=204x-2x^2+3x^2+14x+3 , [0,20]	$f (x) = 204 x - 2 x^{2} + 3 x^{2} + 14 x + 3$ , $[0, 20]$
38108	Find the Average Value of the Function	f(x)=25-x^2 , (0,10)	$f (x) = 25 - x^{2}$ , $(0, 10)$
38109	Find the Average Value of the Function	f(x)=25-x^2 , [0,2]	$f (x) = 25 - x^{2}$ , $[0, 2]$
38110	Find the Average Value of the Function	f(x)=29+8(2.71828182)^(-0.04x) , [0,5]	$f (x) = 29 + 8 {(2.7\overline{1828})}^{- 0.04 x}$ , $[0, 5]$
38111	Find the Average Value of the Function	f(x)=-2x , [-3,-2]	$f (x) = - 2 x$ , $[- 3, - 2]$
38112	Find the Average Value of the Function	f(x)=2x , [1,9]	$f (x) = 2 x$ , $[1, 9]$
38113	Find the Average Value of the Function	f(x)=2x-x^2 , [0,2]	$f (x) = 2 x - x^{2}$ , $[0, 2]$
38114	Find the Average Value of the Function	f(x)=3x-6 , (0,4)	$f (x) = 3 x - 6$ , $(0, 4)$
38115	Find the Average Value of the Function	f(x)=2x+3 , [-1,2]	$f (x) = 2 x + 3$ , $[- 1, 2]$
38116	Find the Average Value of the Function	f(x)=2x-7 , (2,3)	$f (x) = 2 x - 7$ , $(2, 3)$
38117	Find the Average Value of the Function	f(x)=3x^2+3 , [2,4]	$f (x) = 3 x^{2} + 3$ , $[2, 4]$
38118	Find the Average Value of the Function	f(x)=3x^2-x , [-1,4]	$f (x) = 3 x^{2} - x$ , $[- 1, 4]$
38119	Find the Average Value of the Function	f(x)=3-5x , (-1,8)	$f (x) = 3 - 5 x$ , $(- 1, 8)$
38120	Find the Average Value of the Function	f(x)=4-x^2 , [-2,2]	$f (x) = 4 - x^{2}$ , $[- 2, 2]$
38121	Find the Average Value of the Function	f(x)=4-x^2 , [-5,4]	$f (x) = 4 - x^{2}$ , $[- 5, 4]$
38122	Find the Average Value of the Function	f(x)=4x^3 , [-6,6]	$f (x) = 4 x^{3}$ , $[- 6, 6]$
38123	Find the Average Value of the Function	f(x)=4x^3-3x^2 , [0,1]	$f (x) = 4 x^{3} - 3 x^{2}$ , $[0, 1]$
38124	Find the Average Value of the Function	f(x)=4x^3-3x^2 , [-1,2]	$f (x) = 4 x^{3} - 3 x^{2}$ , $[- 1, 2]$
38125	Find the Average Value of the Function	f(x)=400-70x , [0,10]	$f (x) = 400 - 70 x$ , $[0, 10]$
38126	Find the Average Value of the Function	f(x)=49-x^2 , (-7,7)	$f (x) = 49 - x^{2}$ , $(- 7, 7)$
38127	Find the Average Value of the Function	f(x)=4x , [1,5]	$f (x) = 4 x$ , $[1, 5]$
38128	Evaluate the Integral	integral of (x^3)/(x-1) with respect to x	$\int \frac{x^{3}}{x - 1} d x$
38129	Find the Average Value of the Function	f(x)=4x , [1,7]	$f (x) = 4 x$ , $[1, 7]$
38130	Find the Average Value of the Function	f(x)=4x+5 , [2,6]	$f (x) = 4 x + 5$ , $[2, 6]$
38131	Find the Average Value of the Function	f(x)=4x+6 , [-1,4]	$f (x) = 4 x + 6$ , $[- 1, 4]$
38132	Find the Average Value of the Function	f(x)=4x-2 , (1,3)	$f (x) = 4 x - 2$ , $(1, 3)$
38133	Find the Average Value of the Function	f(x)=5x^2+2x-3 , [-3,3]	$f (x) = 5 x^{2} + 2 x - 3$ , $[- 3, 3]$
38134	Find the Average Value of the Function	f(x)=50000+600x , [0,500]	$f (x) = 50000 + 600 x$ , $[0, 500]$
38135	Find the Average Value of the Function	f(x)=5csc(x) , 0<x<2pi	$f (x) = 5 \csc (x)$ , $0 < x < 2 π$
38136	Find the Average Value of the Function	f(x)=6 square root of x , [4,9]	$f (x) = 6 \sqrt{x}$ , $[4, 9]$
38137	Find the Average Value of the Function	f(x)=6 square root of x , [0,4]	$f (x) = 6 \sqrt{x}$ , $[0, 4]$
38138	Find the Average Value of the Function	f(x)=6x^2dx , 0<x<4	$f (x) = 6 x^{2} d x$ , $0 < x < 4$
38139	Find the Average Value of the Function	f(x)=6x^3 , [-5,2]	$f (x) = 6 x^{3}$ , $[- 5, 2]$
38140	Find the Average Value of the Function	f(x)=600-30x , [0,10]	$f (x) = 600 - 30 x$ , $[0, 10]$
38141	Find the Average Value of the Function	f(x)=x^2-15 , [0,9]	$f (x) = x^{2} - 15$ , $[0, 9]$
38142	Find the Average Value of the Function	f(x)=x^2-17 , (0,3)	$f (x) = x^{2} - 17$ , $(0, 3)$
38143	Find the Average Value of the Function	f(x)=x^2-19 , [0,9]	$f (x) = x^{2} - 19$ , $[0, 9]$
38144	Find the Average Value of the Function	f(x)=x^2-23 , [0,3]	$f (x) = x^{2} - 23$ , $[0, 3]$
38145	Find the Average Value of the Function	f(x)=x^2-2x+1 , [0,2]	$f (x) = x^{2} - 2 x + 1$ , $[0, 2]$
38146	Find the Average Value of the Function	f(x)=x^2-3 , [0,3]	$f (x) = x^{2} - 3$ , $[0, 3]$
38147	Find the Average Value of the Function	f(x)=x^2-3x+5 , [-1,2]	$f (x) = x^{2} - 3 x + 5$ , $[- 1, 2]$
38148	Find the Average Value of the Function	f(x)=x^2-4x+1 , [0,3]	$f (x) = x^{2} - 4 x + 1$ , $[0, 3]$
38149	Find the Average Value of the Function	f(x)=x^2-6 , [0,5]	$f (x) = x^{2} - 6$ , $[0, 5]$
38150	Find the Average Value of the Function	f(x)=x^2-6x+8 , [0,6]	$f (x) = x^{2} - 6 x + 8$ , $[0, 6]$
38151	Find the Average Value of the Function	f(x)=x^2-7 , [0,1]	$f (x) = x^{2} - 7$ , $[0, 1]$
38152	Find the Average Value of the Function	f(x)=x^2-9 , [0,3]	$f (x) = x^{2} - 9$ , $[0, 3]$
38153	Find the Average Value of the Function	f(x)=x^3 , (5,125)	$f (x) = x^{3}$ , $(5, 125)$
38154	Find the Average Value of the Function	f(x)=x^3 , [0,1]	$f (x) = x^{3}$ , $[0, 1]$
38155	Find the Average Value of the Function	f(x)=x^3-3x^2 , [0,4]	$f (x) = x^{3} - 3 x^{2}$ , $[0, 4]$
38156	Find the Average Value of the Function	f(x)=x^3-4x^2+5x , [1,2]	$f (x) = x^{3} - 4 x^{2} + 5 x$ , $[1, 2]$
38157	Evaluate the Integral	integral of (y^3-y-1)/((y-1)(y^2-y)) with respect to y	$\int \frac{y^{3} - y - 1}{(y - 1) (y^{2} - y)} d y$
38158	Find the Average Value of the Function	f(x)=100-x^2 , [-10,0]	$f (x) = 100 - x^{2}$ , $[- 10, 0]$
38159	Find the Average Value of the Function	f(x)=100-x , [-10,0]	$f (x) = 100 - x$ , $[- 10, 0]$
38160	Find the Average Value of the Function	f(x)=2 , [1,4]	$f (x) = 2$ , $[1, 4]$
38161	Find the Average Value of the Function	f(x)=6x-12 , [1,5]	$f (x) = 6 x - 12$ , $[1, 5]$
38162	Find the Average Value of the Function	f(x)=7x^2+7 , [-1,4]	$f (x) = 7 x^{2} + 7$ , $[- 1, 4]$
38163	Find the Average Value of the Function	f'(x)=8x^2+3x-9 , (0,5)	$f' (x) = 8 x^{2} + 3 x - 9$ , $(0, 5)$
38164	Find the Average Value of the Function	f(x)=8x^4+2x^3+4x-9 , [-2,-1]	$f (x) = 8 x^{4} + 2 x^{3} + 4 x - 9$ , $[- 2, - 1]$
38165	Find the Average Value of the Function	f(x)=8-x , [1,4]	$f (x) = 8 - x$ , $[1, 4]$
38166	Find the Average Value of the Function	f(x)=8x+9 , [5,8]	$f (x) = 8 x + 9$ , $[5, 8]$
38167	Find the Average Value of the Function	f(x)=9-x^2 , [0,6]	$f (x) = 9 - x^{2}$ , $[0, 6]$
38168	Find the Average Value of the Function	f(x)=9-x^2 , [-3,3]	$f (x) = 9 - x^{2}$ , $[- 3, 3]$
38169	Find the 2nd Derivative	f(x)=1/(12x^2)	$f (x) = \frac{1}{12 x^{2}}$
38170	Find the Average Value of the Function	f(x)=9x^3 , [-10,10]	$f (x) = 9 x^{3}$ , $[- 10, 10]$
38171	Find the Average Value of the Function	f(x)=ax+b , [0,2]	$f (x) = a x + b$ , $[0, 2]$
38172	Find the Average Value of the Function	f(x)=(ex)/7 , [0,7]	$f (x) = \frac{e x}{7}$ , $[0, 7]$
38173	Find the Average Value of the Function	f(x)=sin(2x) , 0=x=pi/2	$f (x) = \sin (2 x)$ , $0 = x = \frac{π}{2}$
38174	Find the Average Value of the Function	f(x)=sin(5x) , 0=x=pi/5	$f (x) = \sin (5 x)$ , $0 = x = \frac{π}{5}$
38175	Find the Average Value of the Function	f(x)=sin(nx) , 0=x=pi/n	$f (x) = \sin (n x)$ , $0 = x = \frac{π}{n}$
38176	Find the Average Value of the Function	f(x)=sin(x) , [0,pi]	$f (x) = \sin (x)$ , $[0, π]$
38177	Find the Average Value of the Function	f(x)=x+12x^-1 , [-4,-3]	$f (x) = x + 12 x^{- 1}$ , $[- 4, - 3]$
38178	Evaluate the Summation	sum from n=1 to 9 of 3*2^n	$\sum_{n = 1}^{9} 3 \cdot 2^{n}$
38179	Find the Average Value of the Function	f'(x)=x square root of 1-x^2 , (0,5/3)	$f' (x) = x \sqrt{1 - x^{2}}$ , $(0, \frac{5}{3})$
38180	Find the Average Value of the Function	f(x)=x square root of 4-x^2 , [-2,2]	$f (x) = x \sqrt{4 - x^{2}}$ , $[- 2, 2]$
38181	Find the Average Value of the Function	f(x)=x-x^2 , [0,2]	$f (x) = x - x^{2}$ , $[0, 2]$
38182	Find the Average Value of the Function	f(x) = square root of x , [0,25]	$f (x) = \sqrt{x}$ , $[0, 25]$
38183	Find the Average Value of the Function	f(x) = square root of x+1 , [0,24]	$f (x) = \sqrt{x + 1}$ , $[0, 24]$
38184	Find the Average Value of the Function	f(x) = cube root of x , (1,8)	$f (x) = \sqrt[3]{x}$ , $(1, 8)$
38185	Find the Average Value of the Function	f(x) = cube root of x , [1,27]	$f (x) = \sqrt[3]{x}$ , $[1, 27]$
38186	Find the Average Value of the Function	f(x)=(2x^(3/2))/3+C , 0<x<4	$f (x) = \frac{2 x^{\frac{3}{2}}}{3} + C$ , $0 < x < 4$
38187	Find the Average Value of the Function	f(x)=x/4 , [1,5]	$f (x) = \frac{x}{4}$ , $[1, 5]$
38188	Find the Average Value of the Function	f(x)=2x^2+5x+3 , -1<x<2	$f (x) = 2 x^{2} + 5 x + 3$ , $- 1 < x < 2$
38189	Find the Average Value of the Function	f(x)=2x-x^2 , [-1,1]	$f (x) = 2 x - x^{2}$ , $[- 1, 1]$
38190	Find the Average Value of the Function	g(x)=(x-6)^2 , [5,8]	$g (x) = {(x - 6)}^{2}$ , $[5, 8]$
38191	Find the Average Value of the Function	g(x)=x^2 square root of 1+x^3 , [0,2]	$g (x) = x^{2} \sqrt{1 + x^{3}}$ , $[0, 2]$
38192	Find the Average Value of the Function	g(x)=x^2(x^4-3) , [0,2]	$g (x) = x^{2} (x^{4} - 3)$ , $[0, 2]$
38193	Find the Average Value of the Function	p(x) = natural log of -x^2+3x^2+72x+1 , 0<x<10	$p (x) = \ln (- x^{2} + 3 x^{2} + 72 x + 1)$ , $0 < x < 10$
38194	Find the Average Value of the Function	f(x)=x^2 , (0,2)	$f (x) = x^{2}$ , $(0, 2)$
38195	Find the Average Value of the Function	f(x)=x^2+1 , -1<x<2	$f (x) = x^{2} + 1$ , $- 1 < x < 2$
38196	Find the Average Value of the Function	f(x)=x^2+2 , [0,4]	$f (x) = x^{2} + 2$ , $[0, 4]$
38197	Find the Average Value of the Function	f(x)=x^2+2x , 0<x<6	$f (x) = x^{2} + 2 x$ , $0 < x < 6$
38198	Find the Average Value of the Function	f(x)=x^2+2x+10 , [-2,6]	$f (x) = x^{2} + 2 x + 10$ , $[- 2, 6]$
38199	Find the Average Value of the Function	f(x)=-x^2+3x+38 , [0,9]	$f (x) = - x^{2} + 3 x + 38$ , $[0, 9]$
38200	Find the Average Value of the Function	f(x)=x^2+4x+2 , (-3,-2)	$f (x) = x^{2} + 4 x + 2$ , $(- 3, - 2)$