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

Evaluate the integral of (Sin^5x + Cos 3x)dx from x = 0 to x = pi/2.

If g(x) = integral of 5Cost / t dt from 3 to sq.rt x, find g’(x) by using the fundamental theorem of calculus.

Evaluate the integral of (7x^3 - 4x^2) dx.

Find the area bounded by the curve at the 2nd and 3rd quadrant x = t^2 – 1, y = 5t^3 (t^2 – 1).

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

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

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

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

Find the length of arc of r = 2/(1+cos theta) from theta = 0 to theta = π/2.

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.

What is the area bounded by the curve y=tan² x and the lines y=0 and x = π/2?

Find the volume formed by revolving the triangle whose vertices are (1,1), (2,4) and (3,1) about the line 2x-5y = 10.

Find the centroid of the solid formed by revolving about x = 2 bounded by y = x^3, x = 2 and y = 0.

Determine the moment of inertia enclosed by the curve x^2 + y^2 = 36 with respect to the line y = 8.

A rectangular plate 6 m by 8 m is submerged vertically in water. Find the force on one face if the shorter side is uppermost and lies in the surface of the liquid.

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 x^2 – 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 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.

Evaluate integral lnxdx from 1 to e.

Find the mass of lamina in the given region with density function: D[(x, y)], 0 < or equal x < or equal π/2, 0 < or equal y < or equal cos x and ρ = 7x.

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 length of the arc described by the parabola x^2 = 4y from x = -2 to x =2.

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

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.

Determine the height of the centroid of the semi-circle with radius a from its diameter.

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