What is the integral from 2 to 0 of cx ?

The integral from 2 to 0 of cx is -c*2

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integral from 2 to 0 of cx

\int_{2}^{0} c x d x

- c \cdot 2

Solution steps

\int_{2}^{0} c x d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{2} c x d x

Take the constant out:

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

= - c \cdot \int_{0}^{2} x d x

Apply the Power Rule

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

= - c [\frac{x ^{2}}{2}]_{0}^{2}

Compute the boundaries:

2

= - c \cdot 2

\int_{0}^{1} \frac{2}{x ^{3}} d x

\int_{0}^{1} - \frac{( x - 1 ) ^{3}}{3} d x

\int_{0}^{1} 2 π (2 - x) (x - x^{2}) d x

\int_{- 4}^{0} (- x^{2} - 4 x) d x

\int_{- 1}^{1} x^{3} - 1 d x