What is the integral from 0 to 1 of (1-x^2)sin(x) ?

The integral from 0 to 1 of (1-x^2)sin(x) is 3-2cos(1)-2sin(1)

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integral from 0 to 1 of (1-x^2)sin(x)

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

3 - 2 cos (1) - 2 sin (1)

Decimal

0.23645 \dots

Solution steps

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

Expand

(1 - x^{2}) sin (x) : sin (x) - x^{2} sin (x)

= \int_{0}^{1} sin (x) - x^{2} sin (x) 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_{0}^{1} sin (x) d x - \int_{0}^{1} x^{2} sin (x) d x

\int_{0}^{1} sin (x) d x = - cos (1) + 1

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

= - cos (1) + 1 - (cos (1) + 2 sin (1) - 2)

Simplify

- cos (1) + 1 - (cos (1) + 2 sin (1) - 2) : 3 - 2 cos (1) - 2 sin (1)

= 3 - 2 cos (1) - 2 sin (1)

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

\int_{0}^{1} 3 3 x d x

\int_{1}^{2} 2 y d y

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

\int_{0}^{6} (36 - x^{2}) d x

What is the integral from 0 to 1 of (1-x^2)sin(x) ?
The integral from 0 to 1 of (1-x^2)sin(x) is 3-2cos(1)-2sin(1)