What is the integral from 0 to 3 of 30(25-t^2) ?

The integral from 0 to 3 of 30(25-t^2) is 1980

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integral from 0 to 3 of 30(25-t^2)

\int_{0}^{3} 30 (25 - t^{2}) d t

1980

Solution steps

\int_{0}^{3} 30 (25 - t^{2}) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 30 \cdot \int_{0}^{3} 25 - t^{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

= 30 (\int_{0}^{3} 25 d t - \int_{0}^{3} t^{2} d t)

\int_{0}^{3} 25 d t = 75

\int_{0}^{3} t^{2} d t = 9

= 30 (75 - 9)

Simplify

= 1980

x \to \infty lim (∣ x + 2 ∣)

\int_{0}^{\infty} \frac{1}{2 x + 5} d x

\int_{0}^{1} \frac{1}{2 t ^{2} - 2 t + 1} d t

\frac{1}{1 - x ^{2}}, 0

\frac{d}{d x} (- \frac{x}{5})

What is the integral from 0 to 3 of 30(25-t^2) ?
The integral from 0 to 3 of 30(25-t^2) is 1980