Q27 of 29 Page 1

Evaluate

OR


Evaluate .

Let I =

Here, we express the denominator in terms (sin x – cos x) which is the integration of numerator.


Clearly,



Therefore, becomes,




Let, sin x – cos x = t.


Then, d(sin x – cos x) = dt


(cos x + sin x)dx = dt.


Also x = 0


t = sin0 – cos0 = – 1 and x =



∴





OR


(let)


When ; a = 1, b = 3











As ∴







More from this chapter

All 29 →
25

If matrix A = , find A–1. Use it to solve the system of equations.

2x – 3y + 5z = 11


3x + 2y – 4z = 0


x + y – 2z = – 3.


OR


Using elementary row transformations, find the inverse of the matrix A = .

 26

Using integration, find the area of the region in the first quadrant enclosed by the x – axis, the line y = x and the circle x2 + y2 = 32.

 28

Find the distance of the point ( – 1, – 5, – 10) from the point of intersection of the line and the plane

29

A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand – operated. It takes 4 minutes on the automatic and 6 minutes on the hand operated machines to manufacture a packet of screws ‘B’. Each machine is availble for at most 4 hours on any day. The manufacturer can sell a packet of screws ‘A’ at a profit of 70 paise and screws ‘B’ at a profit of Rs. 1. Assuming that he can sell all the screws he manufactrures, how many packets of each type should the factory owner produce in a day in order to maximize his profit ? Formulate the above LPP and solve it graphically and find the maximum profit.