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

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

Popular >

integral from 0 to 1 of cos^3(x)

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

sin (1) - \frac{sin ^{3} ( 1 )}{3}

Decimal

0.64286 \dots

Solution steps

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

Rewrite using trig identities

= \int_{0}^{1} (1 - sin^{2} (x)) cos (x) d x

Apply u-substitution

: \int_{0}^{s i n (1)} 1 - u^{2} d u

= \int_{0}^{s i n (1)} 1 - u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{s i n (1)} 1 d u - \int_{0}^{s i n (1)} u^{2} d u

\int_{0}^{s i n (1)} 1 d u = sin (1)

\int_{0}^{s i n (1)} u^{2} d u = \frac{sin ^{3} ( 1 )}{3}

= sin (1) - \frac{sin ^{3} ( 1 )}{3}

\int_{0}^{\frac{π}{2}} 10 + sin (x) - x^{2} d x

\int_{0}^{2} 8 x^{2} e^{2 x} d x

\int_{0}^{l n (2)} 2 e^{2 x} d x

\int_{0}^{\frac{1}{2}} 1 + 4 x^{2} d x

\int_{9}^{16} (- x^{- \frac{1}{2}} + 5) d x

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