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Popular >

integral from 0 to 2 of 4x^2+x+5

Solution

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

Solution

\frac{68}{3}

+1

Decimal Notation

22.66666 \dots

Solution steps

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

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} x d x = 2

\int_{0}^{2} 5 d x = 10

= \frac{32}{3} + 2 + 10

Simplify

\frac{32}{3} + 2 + 10 : \frac{68}{3}

= \frac{68}{3}

Popular Examples

integral from 0 to 1/7 of arcsin(7x)

\int_{0}^{\frac{1}{7}} arcsin (7 x) d x

integral from 0 to pi/2 of 3sin(2x)

\int_{0}^{\frac{π}{2}} 3 sin (2 x) d x

integral from 0 to 1 of sqrt(x-1)

\int_{0}^{1} x - 1 d x

integral from 0 to pi/2 of tcos(t)

\int_{0}^{\frac{π}{2}} t cos (t) d t

integral from 0 to 2 of 4xsin(n)x

\int_{0}^{2} 4 x sin (n) x d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of 4x^2+x+5 ?
The integral from 0 to 2 of 4x^2+x+5 is 68/3