What is the integral from x^2 to x of sin(xy) ?

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

Popular >

integral from x^2 to x of sin(xy)

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

\frac{- cos ( x ^{2} ) + cos ( x ^{3} )}{x}

Solution steps

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

Apply u-substitution

: \int_{x^{3}}^{x^{2}} \frac{sin ( u )}{x} d u

= \int_{x^{3}}^{x^{2}} \frac{sin ( u )}{x} d u

Take the constant out:

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

= \frac{1}{x} \cdot \int_{x^{3}}^{x^{2}} sin (u) d u

Use the common integral:

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

= \frac{1}{x} [- cos (u)]_{x^{3}}^{x^{2}}

Compute the boundaries:

- cos (x^{2}) + cos (x^{3})

= \frac{1}{x} (- cos (x^{2}) + cos (x^{3}))

Simplify

= \frac{- cos ( x ^{2} ) + cos ( x ^{3} )}{x}

\int_{0}^{6} x^{2} + 1 d x

\int_{0}^{\frac{l}{2}} x sin (\frac{nπ x}{l}) d x

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

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

\int_{0}^{1} \frac{5 x ^{4}}{x ^{5} + 6} d x

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