Definite Integral/Examples
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Examples of Definite Integrals
Definite Integral of $2 x$ from $2$ to $3$
- $\ds \int_2^3 2 x \rd x = 5$
Definite Integral of $x^2$ from $0$ to $2$
- $\ds \int_0^2 x^2 \rd x = \dfrac 8 3$
Definite Integral of $\sqrt x$ from $0$ to $4$
- $\ds \int_0^4 \sqrt x \rd x = \dfrac {16} 3$
Definite Integral of $\cos x$ from $0$ to $\dfrac \pi 2$
- $\ds \int_0^{\pi / 2} \cos x \rd x = 1$
Definite Integral of $\dfrac 1 x$ from $1$ to $e$
- $\ds \int_1^e \dfrac {\d x} x = 1$
Definite Integral of $\dfrac 1 {1 - x}$ from $2$ to $3$
- $\ds \int_2^3 \dfrac {\d x} {1 - x} = \ln \dfrac 1 2$