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Popular >

integral from 1 to 2 of (4-r^2)r

Solution

\int_{1}^{2} (4 - r^{2}) r d r

Solution

\frac{9}{4}

+1

Decimal Notation

2.25

Solution steps

\int_{1}^{2} (4 - r^{2}) r d r

Expand

(4 - r^{2}) r : 4 r - r^{3}

= \int_{1}^{2} 4 r - r^{3} d r

Apply the Sum Rule:

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

= \int_{1}^{2} 4 r d r - \int_{1}^{2} r^{3} d r

\int_{1}^{2} 4 r d r = 6

\int_{1}^{2} r^{3} d r = \frac{15}{4}

= 6 - \frac{15}{4}

Simplify

6 - \frac{15}{4} : \frac{9}{4}

= \frac{9}{4}

Popular Examples

integral from 2 to 4 of (ln(x))^3

\int_{2}^{4} (ln (x))^{3} d x

integral from 0 to 1 of (12)/(x^2-9)

\int_{0}^{1} \frac{12}{x ^{2} - 9} d x

integral from 0 to 1 of sqrt(2-2cos(x))

\int_{0}^{1} 2 - 2 cos (x) d x

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

\int_{0}^{1} \frac{1}{x ^{2} + 2 x} d x

integral from 0 to pi/(24) of xtan^2(8x)

\int_{0}^{\frac{π}{24}} x tan^{2} (8 x) d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of (4-r^2)r ?
The integral from 1 to 2 of (4-r^2)r is 9/4