What is the integral from-5 to 5 of 1/2 (25^2-x^4) ?

The integral from-5 to 5 of 1/2 (25^2-x^4) is 2500

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integral from-5 to 5 of 1/2 (25^2-x^4)

\int_{- 5}^{5} \frac{1}{2} (2 5^{2} - x^{4}) d x

2500

Solution steps

\int_{- 5}^{5} \frac{1}{2} (2 5^{2} - x^{4}) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{- 5}^{5} 2 5^{2} - x^{4} d x

Simplify

= \frac{1}{2} \cdot \int_{- 5}^{5} 625 - x^{4} 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

= \frac{1}{2} (\int_{- 5}^{5} 625 d x - \int_{- 5}^{5} x^{4} d x)

\int_{- 5}^{5} 625 d x = 6250

\int_{- 5}^{5} x^{4} d x = 1250

= \frac{1}{2} (6250 - 1250)

Simplify

\frac{1}{2} (6250 - 1250) : 2500

= 2500

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What is the integral from-5 to 5 of 1/2 (25^2-x^4) ?
The integral from-5 to 5 of 1/2 (25^2-x^4) is 2500