Evaluate
220
Share
Copied to clipboard
\int 3x+7\mathrm{d}x
Evaluate the indefinite integral first.
\int 3x\mathrm{d}x+\int 7\mathrm{d}x
Integrate the sum term by term.
3\int x\mathrm{d}x+\int 7\mathrm{d}x
Factor out the constant in each of the terms.
\frac{3x^{2}}{2}+\int 7\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply 3 times \frac{x^{2}}{2}.
\frac{3x^{2}}{2}+7x
Find the integral of 7 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{3}{2}\times 10^{2}+7\times 10-\left(\frac{3}{2}\times 0^{2}+7\times 0\right)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
220
Simplify.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}