Question

Evaluate the iterated integral from 0 to 1 of the integral from y to sqrt(2-y^2) of 5(x+y) dx dy by converting to polar coordinates.

Answer 1

The cos3 2x integral is like the previous example: ... Find the antiderivatives. 1. ∫ sin2 x dx ⇒. 2. ∫ sin3 x dx ⇒. 3. ∫ sin4 x dx ⇒. 4.

Answer 2

Part a


∞∑n=1(3n)4=∞∑n=134n4=81∞∑n=11n4=81π490∑n


=1∞(3n)4=∑n=1∞34n4=81∑n=1∞1n4=81π490

Part b

∞∑k=61(k−3)4=∞∑k=31((k+3)−3)4[Drop the index


from k=6 to k=3]=∞∑k=31k4=∞∑k=11k4−114−124=π490−1716