What is the integral from 0 to 7 of pi(x+1)^2 ?

The integral from 0 to 7 of pi(x+1)^2 is pi 511/3

Popular >

integral from 0 to 7 of pi(x+1)^2

\int_{0}^{7} π (x + 1)^{2} d x

π \frac{511}{3}

Decimal Notation

535.11794 \dots

Solution steps

\int_{0}^{7} π (x + 1)^{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}^{7} (x + 1)^{2} d x

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

= π \cdot \int_{0}^{7} x^{2} + 2 x + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{0}^{7} x^{2} d x + \int_{0}^{7} 2 x d x + \int_{0}^{7} 1 d x)

\int_{0}^{7} x^{2} d x = \frac{343}{3}

\int_{0}^{7} 2 x d x = 49

\int_{0}^{7} 1 d x = 7

= π (\frac{343}{3} + 49 + 7)

Simplify

π (\frac{343}{3} + 49 + 7) : π \frac{511}{3}

= π \frac{511}{3}

f (x) = x^{2} - 5 x + 3

- 3 y^{^{'}} + \frac{3 y}{x} = \frac{y ^{4}}{x ^{2}}

\frac{\partial}{\partial y} (3 x^{2} y^{2} + 4)

\frac{\partial}{\partial x} (- 8 (x + y + z)^{2})

\int \frac{arcsin ( x )}{( 1 - x ^{2} ) ^{\frac{1}{2}}} d x

What is the integral from 0 to 7 of pi(x+1)^2 ?
The integral from 0 to 7 of pi(x+1)^2 is pi 511/3