What is the integral from 0 to 4 of 5x ?

The integral from 0 to 4 of 5x is 40

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integral from 0 to 4 of 5x

\int_{0}^{4} 5 x d x

40

Solution steps

\int_{0}^{4} 5 x d x

Take the constant out:

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

= 5 \cdot \int_{0}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{4}

= 5 [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= 5 \cdot 8

Simplify

= 40

x \to 0 + lim (ln (tan (x)))

\frac{d}{d x} (arcsec (x) - 7 x)

\int \frac{1}{2 y - y ^{2}} d y

y = 2 x^{3} - 5 x + 1, (- 1, 4)

\int \frac{3 x}{x - 1} d x