en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 6 of (8x-1)^2

Solution

\int_{0}^{6} (8 x - 1)^{2} d x

Solution

4326

Solution steps

\int_{0}^{6} (8 x - 1)^{2} d x

Expand

(8 x - 1)^{2} : 64 x^{2} - 16 x + 1

= \int_{0}^{6} 64 x^{2} - 16 x + 1 d x

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}^{6} 64 x^{2} d x - \int_{0}^{6} 16 x d x + \int_{0}^{6} 1 d x

\int_{0}^{6} 64 x^{2} d x = 4608

\int_{0}^{6} 16 x d x = 288

\int_{0}^{6} 1 d x = 6

= 4608 - 288 + 6

Simplify

= 4326

Graph

Popular Examples

integral from 0 to b of 10x^2

\int_{0}^{b} 10 x^{2} d x

integral from-1 to 2 of (5x^3+2x^2-x)

\int_{- 1}^{2} (5 x^{3} + 2 x^{2} - x) d x

integral from 3 to 3x+5 of t/(1+t^3)

\int_{3}^{3 x + 5} \frac{t}{1 + t ^{3}} d t

integral from 0 to pi/(30) of cos(5x)

\int_{0}^{\frac{π}{30}} cos (5 x) d x

integral from 1 to infinity of e^{-100x}

\int_{1}^{\infty} e^{- 100 x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of (8x-1)^2 ?
The integral from 0 to 6 of (8x-1)^2 is 4326