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

The integral from 1 to 3 of 25-(t-5)^2 is 94/3

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integral from 1 to 3 of 25-(t-5)^2

\int_{1}^{3} 25 - (t - 5)^{2} d t

\frac{94}{3}

Decimal

31.33333 \dots

Solution steps

\int_{1}^{3} 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}^{3} 25 d t - \int_{1}^{3} (t - 5)^{2} d t

\int_{1}^{3} 25 d t = 50

\int_{1}^{3} (t - 5)^{2} d t = \frac{56}{3}

= 50 - \frac{56}{3}

Simplify

50 - \frac{56}{3} : \frac{94}{3}

= \frac{94}{3}

What is the integral from 1 to 3 of 25-(t-5)^2 ?
The integral from 1 to 3 of 25-(t-5)^2 is 94/3