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

The integral from 1 to 3 of xsin(x^2) is 1/2 (-cos(9)+cos(1))

Popular >

integral from 1 to 3 of xsin(x^2)

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

\frac{1}{2} (- cos (9) + cos (1))

Decimal Notation

0.72571 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{9} \frac{sin ( u )}{2} d u

= \int_{1}^{9} \frac{sin ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{9} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{1}^{9}

Compute the boundaries:

- cos (9) + cos (1)

= \frac{1}{2} (- cos (9) + cos (1))

\int_{0}^{2} (4 x - 1) (2 x^{2} - x)^{4} d x

\int_{10 x - 500}^{1500} \frac{1}{75000} d y

\int_{x^{2}}^{x} (x + y) d y

\int_{- \frac{π}{2}}^{\frac{π}{2}} sin (t) d t

What is the integral from 1 to 3 of xsin(x^2) ?
The integral from 1 to 3 of xsin(x^2) is 1/2 (-cos(9)+cos(1))