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Popular >

integral from 1 to 4 of x(1+x)

Solution

\int_{1}^{4} x (1 + x) d x

Solution

\frac{57}{2}

+1

Decimal

28.5

Solution steps

\int_{1}^{4} x (1 + x) d x

Expand

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

= \int_{1}^{4} x + x^{2} 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

= \int_{1}^{4} x d x + \int_{1}^{4} x^{2} d x

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

\int_{1}^{4} x^{2} d x = 21

= \frac{15}{2} + 21

Simplify

\frac{15}{2} + 21 : \frac{57}{2}

= \frac{57}{2}

Graph

Popular Examples

integral from 0 to 3/4 of 1/(16x^2+9)

\int_{0}^{\frac{3}{4}} \frac{1}{16 x ^{2} + 9} d x

integral from pi/2 to pi of-xcos(x)

\int_{\frac{π}{2}}^{π} - x cos (x) d x

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

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

integral from 0 to 0.1 of 1

\int_{0}^{0.1} 1 d x

integral from 0 to 2 of cos(x^2)x

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

Frequently Asked Questions (FAQ)

What is the integral from 1 to 4 of x(1+x) ?
The integral from 1 to 4 of x(1+x) is 57/2