Calculus Answers

Determine the length of curve 𝑦 = log(sec 𝑥) between 0 ≤ 𝑥 ≤

𝜋

4

Find the area of region bounded between the parabola and line given below:

a. y2 = 2x and y = 2x.

b. y2 = 4x and y = 2x.

c. y2 = 4ax and y = x.

d. y2 = 2kx and y = mx.

Find area bounded by parabola y2 = 4ax and line y = mx.

Find the area of the region lying above X-axis and included between the circle 

x2 + y2 = 2ax and the parabola y2 = ax lying above X-axis

Find the area common to the parabolas y2 = 4x and x2 = 4y.

Evaluate the area between y = x2 and the line y = 2x.

Find the area bounded by the parabola y2 = 4ax and its latus rectum.

Find the area of the circle x2 + y2 = r2.

Find the area enclosed between the curve y = x2 + 2, X-axis, x = 3 and x = 4

If𝑓(𝑥,𝑦)=10𝑥5−3𝑥2𝑦6−4𝑦4.𝐹𝑖𝑛𝑑𝑓 (𝑥,𝑦),𝑓 (𝑥,𝑦), 𝑥𝑥 𝑥𝑦 𝑓 (1, −2), 𝑓 (1, 2)