


Ex 7.5
Ex 7.5, 2
Ex 7.5, 3 Important
Ex 7.5, 4
Ex 7.5, 5
Ex 7.5, 6 Important
Ex 7.5, 7 Important
Ex 7.5, 8 You are here
Ex 7.5, 9 Important
Ex 7.5, 10
Ex 7.5, 11 Important
Ex 7.5, 12
Ex 7.5, 13 Important
Ex 7.5, 14 Important
Ex 7.5, 15
Ex 7.5, 16 Important
Ex 7.5, 17
Ex 7.5, 18 Important
Ex 7.5, 19
Ex 7.5, 20 Important
Ex 7.5, 21 Important
Ex 7.5, 22 (MCQ)
Ex 7.5, 23 (MCQ) Important
Ex 7.5, 8 1 2 ( + 2) We can write the integrand as 1 2 ( + 2) = 1 + 1 2 + + 2 1 2 ( + 2) = 1 + 2 + + 2 + 1 2 1 + 1 2 + 3 By cancelling denominator = 1 +2 + +2 + 1 2 Putting x = 2, in (1) 2 = A 2 1 2+2 + B 2+2 + C 2 1 2 2 = A 0+B 0+C 3 2 2 = 9C C = 2 9 Putting x = 1, in (1) 1 = A 1 1 1+2 + B 1+2 + C 1 1 2 1 = A 0 + B 3 + C 1 1 2 1 = 3B B = 1 3 Putting x = 0, in (1) 0= 0 1 0+2 + 0+2 + 0 1 2 0= 1 2 +2 + 0= 2 + 2 3 2 9 0= 2 + 4 9 2 = 4 9 = 4 18 = 2 9 Hence we can write 1 2 ( + 2) = 2 9 1 + 1 3 1 2 + 2 9 + 2 = 2 9 1 + 1 3 1 2 + 2 9 + 2 = 2 9 1 + 1 3 1 2 + 2 9 + 2 = 2 9 log 1 + 1 3 1 1 2 9 log +2 + = 2 9 log 1 2 9 log +2 1 3 1 + = 2 9 log 1 log +2 1 3 1 + = + +