Question

Evaluate the line integral where c is the line segment from (0 3) to (4 6)

Answer 1

x = cost, y = sint, 0 ≤ t ≤ π. It follows that dx dt . = −sint, dy dt. = cost. Therefore,. ∫. C xey ds = ∫ π. 0 cos tesin t√. (−sint)2 + (cos t)2 dt.

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