Calculus Examples

$y = e^{- x^{2}}$ , $y = 0$ , $x = 0$ , $x = 1$

Step 1

To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius $f (x)$ and $A = π r^{2}$ .

$V = π \int_{0}^{1} {(f (x))}^{2} d x$ where $f (x) = e^{- x^{2}}$

Step 2

Multiply the exponents in ${(e^{- x^{2}})}^{2}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$V = e^{- x^{2} \cdot 2}$

Step 2.2

Multiply $2$ by $- 1$ .

$V = e^{- 2 x^{2}}$

Step 3