What is the integral from 0 to 4 of pi(sqrt(x))^2 ?

The integral from 0 to 4 of pi(sqrt(x))^2 is pi8

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integral from 0 to 4 of pi(sqrt(x))^2

\int_{0}^{4} π (x)^{2} d x

π 8

Decimal

25.13274 \dots

Solution steps

\int_{0}^{4} π (x)^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{4} (x)^{2} d x

Simplify

(x)^{2} : x

= π \cdot \int_{0}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{4}

= π [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= π 8

y^{^{'}} + 3 y = 15 - e^{t}

x \to 5 - lim (e^{\frac{3}{( 5 - x )}})

\frac{d}{d x} (csc^{7} (x))

y = (x^{2} - 35)^{7}, at x = 6

f (x) = \frac{2 x ^{2}}{( 1 - 2 x ) 4}, at x = 2

What is the integral from 0 to 4 of pi(sqrt(x))^2 ?
The integral from 0 to 4 of pi(sqrt(x))^2 is pi8