What is the integral from 0 to pi/2 of 3sin(t)cos(t) ?

The integral from 0 to pi/2 of 3sin(t)cos(t) is 3/2

Popular >

integral from 0 to pi/2 of 3sin(t)cos(t)

\int_{0}^{\frac{π}{2}} 3 sin (t) cos (t) d t

\frac{3}{2}

Decimal Notation

1.5

Solution steps

\int_{0}^{\frac{π}{2}} 3 sin (t) cos (t) d t

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{2}} sin (t) cos (t) d t

Apply u-substitution

: \int_{0}^{1} u d u

= 3 \cdot \int_{0}^{1} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{1}

= 3 [\frac{u ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= 3 \cdot \frac{1}{2}

Simplify

= \frac{3}{2}

\int_{0}^{\frac{π}{4}} cos (x^{3}) d x

\int_{1}^{4} 25 - x^{2} d x

\int_{1}^{5} ln (t^{2} + 5 t + 1) d t

\int_{0}^{3} (x^{2} - 2 x y + y^{2}) d y

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

What is the integral from 0 to pi/2 of 3sin(t)cos(t) ?
The integral from 0 to pi/2 of 3sin(t)cos(t) is 3/2