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Popular >

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

Solution

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

Solution

\frac{1}{3}

+1

Solution steps

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

Expand

(2 x - 3)^{2} : 4 x^{2} - 12 x + 9

= \int_{1}^{2} 4 x^{2} - 12 x + 9 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_{1}^{2} 4 x^{2} d x - \int_{1}^{2} 12 x d x + \int_{1}^{2} 9 d x

\int_{1}^{2} 4 x^{2} d x = \frac{28}{3}

\int_{1}^{2} 12 x d x = 18

\int_{1}^{2} 9 d x = 9

= \frac{28}{3} - 18 + 9

Simplify

\frac{28}{3} - 18 + 9 : \frac{1}{3}

= \frac{1}{3}

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y^{^{'}} + 7 y = t + e^{- 4 t}

derivative of 4(3-9x^3)

\frac{d}{d x} (4 (3 - 9 x)^{3})

inverse oflaplace 2/(3s^2+6s+2)inverse laplace

\frac{2}{3 s ^{2} + 6 s + 2}

integral of 1+2sin((x^2)/2)

\int 1 + 2 sin (\frac{x ^{2}}{2}) d x

y^'=-5y+5t^2+2t

y^{^{'}} = - 5 y + 5 t^{2} + 2 t

Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of (2x-3)^2 ?
The integral from 1 to 2 of (2x-3)^2 is 1/3