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

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

Popular >

integral from 0 to 1 of x^2sin(x^3)

\int_{0}^{1} x^{2} sin (x^{3}) d x

\frac{1}{3} (- cos (1) + 1)

Decimal

0.15323 \dots

Solution steps

\int_{0}^{1} x^{2} sin (x^{3}) d x

Apply u-substitution

: \int_{0}^{1} \frac{sin ( u )}{3} d u

= \int_{0}^{1} \frac{sin ( u )}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{0}^{1} sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{3} [- cos (u)]_{0}^{1}

Compute the boundaries:

- cos (1) + 1

= \frac{1}{3} (- cos (1) + 1)

\int_{\frac{π}{2}}^{π} (cos (x)) d x

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

\int_{1}^{e^{3}} \frac{10 ln ( x )}{x} d x

\int_{0}^{1} (5 x^{e} + 9 e^{x}) d x

\int_{1.6}^{5.6} (ln (x + 8) - 2 x) d x

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