Integral of sinxcos3x dx

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$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos{\left(3 x \right)}\, dx$$

Integral(sin(x)*cos(3*x), (x, 0, 1))

The graph

Plot the graph f(x)

The answer [src]

  1   cos(1)*cos(3)   3*sin(1)*sin(3)
- - + ------------- + ---------------
  8         8                8

$$- \frac{1}{8} + \frac{\cos{\left(1 \right)} \cos{\left(3 \right)}}{8} + \frac{3 \sin{\left(1 \right)} \sin{\left(3 \right)}}{8}$$

  1   cos(1)*cos(3)   3*sin(1)*sin(3)
- - + ------------- + ---------------
  8         8                8

$$- \frac{1}{8} + \frac{\cos{\left(1 \right)} \cos{\left(3 \right)}}{8} + \frac{3 \sin{\left(1 \right)} \sin{\left(3 \right)}}{8}$$

-1/8 + cos(1)*cos(3)/8 + 3*sin(1)*sin(3)/8

Numerical answer [src]

-0.147331256528834

-0.147331256528834

The graph

Use the examples entering the upper and lower limits of integration.