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

The integral from 1 to cos(x) of 3t^2 is cos^3(x)-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to cos(x) of 3t^2

\int_{1}^{c o s (x)} 3 t^{2} d t

cos^{3} (x) - 1

Solution steps

\int_{1}^{c o s (x)} 3 t^{2} d t

Take the constant out:

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

= 3 \cdot \int_{1}^{c o s (x)} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{1}^{c o s (x)}

= 3 [\frac{t ^{3}}{3}]_{1}^{c o s (x)}

Compute the boundaries:

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

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

Simplify

= cos^{3} (x) - 1

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

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

\int_{x}^{3 π} sin (t^{2}) d t

\int_{0}^{1} θ x^{θ - 1} d x

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

What is the integral from 1 to cos(x) of 3t^2 ?
The integral from 1 to cos(x) of 3t^2 is cos^3(x)-1