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Popular >

integral from 0 to 6 of (4t-1)^2

Solution

\int_{0}^{6} (4 t - 1)^{2} d t

Solution

1014

Solution steps

\int_{0}^{6} (4 t - 1)^{2} d t

Expand

(4 t - 1)^{2} : 16 t^{2} - 8 t + 1

= \int_{0}^{6} 16 t^{2} - 8 t + 1 d t

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} 16 t^{2} d t - \int_{0}^{6} 8 t d t + \int_{0}^{6} 1 d t

\int_{0}^{6} 16 t^{2} d t = 1152

\int_{0}^{6} 8 t d t = 144

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

= 1152 - 144 + 6

Simplify

= 1014

Graph

Popular Examples

integral from 3 to 6 of (2x-5)

\int_{3}^{6} (2 x - 5) d x

integral from 0 to 1 of 1/(x^2-4x+5)

\int_{0}^{1} \frac{1}{x ^{2} - 4 x + 5} d x

integral from 1 to 2 of 1/2 y

\int_{1}^{2} \frac{1}{2} y d y

integral from-3 to 5 of-x^2+2x+15

\int_{- 3}^{5} - x^{2} + 2 x + 15 d x

integral from 0 to 2 of x(3x-c)

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of (4t-1)^2 ?
The integral from 0 to 6 of (4t-1)^2 is 1014