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Popular >

integral from 3 to 6 of x^2-x+1

Solution

\int_{3}^{6} x^{2} - x + 1 d x

Solution

\frac{105}{2}

+1

Decimal Notation

52.5

Solution steps

\int_{3}^{6} x^{2} - 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_{3}^{6} x^{2} d x - \int_{3}^{6} x d x + \int_{3}^{6} 1 d x

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} x d x = \frac{27}{2}

\int_{3}^{6} 1 d x = 3

= 63 - \frac{27}{2} + 3

Simplify

63 - \frac{27}{2} + 3 : \frac{105}{2}

= \frac{105}{2}

Popular Examples

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

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

integral from 0 to 1/x of xy

\int_{0}^{\frac{1}{x}} x y d y

integral from 0 to-3 of-x^2-3x

\int_{0}^{- 3} - x^{2} - 3 x d x

integral from-1 to 4 of (4x-3)(x-3)

\int_{- 1}^{4} (4 x - 3) (x - 3) d x

integral from 0 to 5 of (25-x^2)^{1/2}

\int_{0}^{5} (25 - x^{2})^{\frac{1}{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 3 to 6 of x^2-x+1 ?
The integral from 3 to 6 of x^2-x+1 is 105/2