What is the integral from 1 to 2 of 25-(t-5)^2 ?

The integral from 1 to 2 of 25-(t-5)^2 is 38/3

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integral from 1 to 2 of 25-(t-5)^2

\int_{1}^{2} 25 - (t - 5)^{2} d t

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

\int_{1}^{2} 25 - (t - 5)^{2} 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_{1}^{2} 25 d t - \int_{1}^{2} (t - 5)^{2} d t

\int_{1}^{2} 25 d t = 25

\int_{1}^{2} (t - 5)^{2} d t = \frac{37}{3}

= 25 - \frac{37}{3}

Simplify

25 - \frac{37}{3} : \frac{38}{3}

= \frac{38}{3}

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What is the integral from 1 to 2 of 25-(t-5)^2 ?
The integral from 1 to 2 of 25-(t-5)^2 is 38/3