What is the integral from 0 to x^2 of f(t) ?

The integral from 0 to x^2 of f(t) is (x^4f)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to x^2 of f(t)

\int_{0}^{x^{2}} f (t) d t

\frac{x ^{4} f}{2}

Solution steps

\int_{0}^{x^{2}} f t d t

Take the constant out:

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

= f \cdot \int_{0}^{x^{2}} t d t

Apply the Power Rule

: [\frac{t ^{2}}{2}]_{0}^{x^{2}}

= f [\frac{t ^{2}}{2}]_{0}^{x^{2}}

Compute the boundaries:

\frac{x ^{4}}{2}

= f \frac{x ^{4}}{2}

Simplify

= \frac{x ^{4} f}{2}

\int_{0}^{\infty} 0 d x

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

\int_{0}^{\frac{π}{2}} sin (x) \cdot cos (x) d x

\int_{4}^{6} \frac{x}{50} d x

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

What is the integral from 0 to x^2 of f(t) ?
The integral from 0 to x^2 of f(t) is (x^4f)/2