Evaluate the integral of (cosx)^7 from 0 to π/2,

Evaluate the integral of (1 + 5e^x)/(1 - e^x) dx,

Find the area bounded by the curve sq.rt of x + sq.rt of y = sq.rt of a and the x and y – axis.

The integral of (1/x^p) dx = 1.25 if limits are x = 0 to x= 1. Find the value of p.

Find the area bounded by the polynomial curve y=x^3 - 4x^2 + 3x and the x axis from x= 0 to x=3

Find the surface area of the sphere x^2 + y^2 + z^2 = a^2 intercepted by the cylinder x^2 + y^2 = 2ax.

Evaluate the integral of 1/(1+x^2) dx from negative infinity to positive infinity.

Find the moment of inertia of the area bounded by the curve y^2 = 4x and the line x = 1 WRT the x axis

Find the volume of the solid generated by revolving the area of the circle x^2 + y^2 = 36 on the second quadrant about the line y + 10 = 0

A napkin ring is to be made from a wooden sphere by drilling it along its diameter. If the radius of the sphere is R and that of the hole is r, find the volume of the material left for the napkin ring in terms of its height h.

The area in the first quadrant bounded by a parabola 12y = x2 , the y axis, and the line y = 3, revolved about the line y = 3. What is the generated volume?

What is the area bounded by the curve defined by the equation x2 – 8y = 0 and its latus rectum.

Find the area bounded by the parabolas y = 6x - x^2 and y = x^2 - 2x.

Find the area bounded by the lemniscate of Bernoulli r^= a^2cos 20

Find the area of the region which is bounded by the parabolas y^2 = 4x and x^2 = 4y.

Find the area enclosed by the curve y = coshx and the line y = 0 from x = 0 to x = 1.

Find the area enclosed by the 4 cusps hypocycloid x = acos' 0, y = asin'e.

Find the area under one arc of cycloid x = a(θ - sin θ), y = a(1 - cos θ).

Find the area enclosed by the loop of y2 = 4x2 (1-x).

Find the area bounded by the parabola √𝑥 + √𝑦 = √𝑎 and the line x + y = a

Find the area bounded by the cardioid r = a (1+ cosθ).

Evaluate the integral of 1 / x^0.0001 dx from x = 1 to x = infinity.

Find the area enclosed by y = x^3, 2x + y = 0 and x – y = 6

Find the area bounded by y = Cosx from x = 0 to x = 1

Find the volume of the solid generated when the area bounded by x^2 + y^2 = 36 in the second quadrant is revolved about the line x = 3

Find the volume generated by revolving about the y axis the area bounded by the curve y=(x squared) + 4 and y= 2 (x squared).

Find the volume generated if the area bounded by the curve y = (tan x)(sec x), y=0, x= π/4 is revolved about the x axis.

Find the arc length of the curve r = 3e2^theta from theta = 0 to theta = π/6

The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x=3. What is the volume generated?

Find the volume generated by rotating a circle x^2+y^2+6x+4y+12=0 about the y-axis.

Find the moment of inertia of a solid generated by revolving the area bounded y=x3 , x= 1, x = 2 and y = 0 about x = 0.

If the function f is even and integral of f(x)dx from 0 to a = 5m-1, then integral of f(x)dx from -a to a = ,

If the average value of the function f(x) = 2x^2 on the interval (0,c) is 6, then c =,

If |1 7 f(x)dx = 4 and |1 7 g(x)dx = 2, find |1 7 [3f(x)+2g(x)+1] dx

A solid is formed by revolving about y-axis, the area bounded by the curve x^3 = y, the y-axis and the line y = 8. Find its centroid

Find the area bounded by the curve y = 2 over (x-3) and the lines y = 0, x= 4 and x= 5

Find the area which is inside r2 = 2cos2θ and outside r =1.

Find the area bounded by one arch of the companion to the cycloid x = a theta, y = a(1-cos theta) and the y-axis.

Locate the centroid of the solid generated when the area of x^2 + y^2 = a^2 in the first quadrant and the fourth quadrant by 2x – y = 2a and x = 0 about x = 0,

Evaluate integral of 2r2 sin theta cos2 theta dr, d theta, 0 > r > sin theta, 0 > theta > π/2,

If the area bounded by the curves y = x, x = 2, y = 0, is revolve about the line y = 0, find the moment of inertia of the solid formed with respect to the axis of revolution.

Find Io for the area of the curve r^2 = a^2 cos θ.

Determine the coordinates of the centroid of the area bounded by the curve x2 = -(y - 4), the x axis and the y axis on the first quadrant.

The cross section of a trough is a parabolic segment 8ft wide and 4ft deep. If the trough is filled with liquid weighing 45 lb/cu.ft. find the total force in N on one end.

The inner surface of a tank is in the form f a hemisphere of radius 3m with the diametral plane on top. Determine the total work done in pumping the water to the top of the tank. For water, w = 9.802 kN/cu.m.

Evaluate the integral of sq.rt of (1-Cosx) dx.

Evaluate the integral of x/ sq.rt of (x^2 – 8x) dx.

Interpret the integral as area from x = -3 to x = 3 sq.rt of (9 – x^2) dx

Evaluate the integral of sin^5x cos^3x dx from x = 0 to x = π/2,

Evaluate the integral of 1/(x+2) dx from x = -10 to x = -6,

Evaluate the integral of 1/(x-y) dxdy with inner bounds of 2y to 3y and outer bounds of 0 to 2.

The area bounded by y = x^2 – c^2 and y = c^2 – x^2 is 576. Find the value of C.

The parabola y = x^2 and a line intersect at the point (a, a^2) and origin. Find the value of a if the enclosed area is 27.

Find the area bounded by r = 2 / (1 + cosθ) and cosθ = 0.

Find the area bounded by x = t^2, y = t^4 (t + 2) and the x – axis

Evaluate the line integral of [ sq.rt of y dx + (x –y) dy ] from (0,0) to (1,1),

If g(x) = integral of 5 Cost / t dt from 3 to sq.rt of x, find g(x) using fundamental theorem of calculus

Find the volume generated by the area between y = coshx and the x axis from x = 0 to x = 1 when revolved about the x axis

Find the area bounded by y = x^3 from x= -2 to x= 1

The area enclosed by the ellipse 4x^2 +9y^2 = 36 is revolved about the line x = 3. What is the volume generated?