Evaluate
2\sin(x)
Differentiate w.r.t. x
2\cos(x)
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\int 2\cos(\theta )\mathrm{d}\theta
Evaluate the indefinite integral first.
2\int \cos(\theta )\mathrm{d}\theta
Factor out the constant using \int af\left(\theta \right)\mathrm{d}\theta =a\int f\left(\theta \right)\mathrm{d}\theta .
2\sin(\theta )
Use \int \cos(\theta )\mathrm{d}\theta =\sin(\theta ) from the table of common integrals to obtain the result.
2\sin(x)-2\sin(0)
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.
2\sin(x)
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}