Q19 of 52 Page 1

Find:

Let

We will use integration by parts for solving this integral,

Therefore,

3x + 5 = Ax + Bx + 6A – 3B

Comparing the coefficients, we get,

A + B = 3……(1)

6A – 3B = 5……(2)

Multiplying equation 1 by 6 and subtracting equation 2 from it, we get,

6A + 6B – 6A + 3B = 18 – 5

9B = 13

Putting the value of B in equation 1, we get,

Now,

Hence,

Find:

Using the properties of determinants, prove that

Solve the differential equation: , given that y = 0 when x = 1.

Solve the differential equation: , subject to the initial condition y(0) = 0.

Using integration, find the area of triangle ABC, whose vertices are A(2, 5), B(4, 7), and C(6, 2).

Find the area of the region lying above the x-axis and included between the circle x² + y² = 8x and inside of the parabola y² = 4x.