Question

- What is,
lim n--> ∞ nΣ(k=1) (2+k*(5/n))^3 * 5/n
as a definite integral.

- Solve d/dt x^4∫2 tan (x^2)dx

- What is the area bounded by the curves x = y^2 - 4y and x = 2y - y^2?

Answer 1

for the limit, I get
∫[2,7] x^3 dx

For the derivative of the integral, I get
tan((x^4)^2)*(4x^3)

For the area, the two curves intersect at (0,0) and (-3,3). So the area is
∫[0,3] (2y-y^2)-(y^2-4y) dy = 9