Question

What is the answer to this question

Answer 1

Answer:

  π

Step-by-step explanation:

The integral decomposes into the sum ...

  $\displaystyle\int_{-2}^2{\left(x^3\cos{\dfrac{x}{2}}\right)\sqrt{4-x^2}}\, dx+\dfrac{1}{2}\int_{-2}^2{\sqrt{4-x^2}}\, dx$

The first term of this sum is the integral of an odd function, so is zero. The second term of this sum is 1/2 the area under a semicircle of radius 2, so is ...

  A = (1/2)(1/2)π·2² = π

The value of the integral is π.