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

The integral from-1 to 1 of x^2cos(x) is 4cos(1)-2sin(1)

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integral from-1 to 1 of x^2cos(x)

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

4 cos (1) - 2 sin (1)

Decimal

0.47826 \dots

Solution steps

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

Apply Integration By Parts

: [x^{2} sin (x) - \int 2 x sin (x) d x]_{- 1}^{1}

= [x^{2} sin (x) - \int 2 x sin (x) d x]_{- 1}^{1}

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

= [x^{2} sin (x) - 2 (- x cos (x) + sin (x))]_{- 1}^{1}

Compute the boundaries:

4 cos (1) - 2 sin (1)

= 4 cos (1) - 2 sin (1)

\int_{0}^{0.5} \frac{1}{( 1 - x ) ^{2}} d x

\int_{1}^{1.5} 1 + 36 x d x

\int_{0}^{4} x + 2 - x d x

\int_{- 1}^{4} (3 x^{4} - 5 x^{3} - x - 6) d x

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

What is the integral from-1 to 1 of x^2cos(x) ?
The integral from-1 to 1 of x^2cos(x) is 4cos(1)-2sin(1)