Calculus Answers

Find constants a and b in the function f(x)=axe^(bx)such that f(1/4)=1 and the function has a local maximum at x=1/4.

Maya is 2 km offshore in a boat and wishes to reach a coastal village which is 6 km down a straight
shoreline from the point on the shore nearest to the boat. She can row at 2 km/hr and run at 5
km/hr. Where should she land her boat to reach the village in the least amount of time?

Calculate the following line integral:
∫ C xy^3dx, where C is the unit circle x^2+y^2=1, oriented counterclockwise. Note: C is at the bottom right of the integral.

The magnitude of the acceleration of a particle which moves along the curve x=2 sin ¡3t,y=2 cos ¡3t and z=8t at any time t>0 is

Show that the base Area of Cylinder (Disc) = πR^2
(cylindrical coordinate system)

Show that the surface Area of Cylinder = 2πRH
(cylindrical coordinate system)

Evaluating Integrals

7.Integral of (3c^2x^2-d^4)^2 dx
8. Integral of (square root of 2x + 2x square root of x + 1/ square root of x) dx
9. Integral of t^3 + 2t^2- 3 / cube root of t

Evaluate The integrals.

5. Integral of t^2 + 3t + 1/t^2 dt
6. Integral of (2x^3-1)(1/ x^2 + 5)

Evaluate Integrals. Show complete solution.

3. Integral of 1/ 2u^2 minus 3u^3/2 minus 2u^5/ 3 du
4. Integral of 2t^6 + 5t^2 +7 / t^2 dt

Evaluate the following integrals. Show complete solution.

1. Integral of 3dy/ y raised to the fourth power
2. Integral of square root of x minus x/3 plus 2/ square root of x dx