Chapter 7 Integrals Ex 7.5 Solutions
Question - 1 : - 
Answer - 1 : - Let 
Equating the coefficientsof x and constant term, we obtain
A + B =1
2A + B =0
On solving, we obtain
A =−1 and B = 2
Answer - 2 : - Let 
Equating the coefficientsof x and constant term, we obtain
A + B =0
−3A + 3B =1
Onsolving, we obtain
Answer - 3 : - Let 
Substituting x =1, 2, and 3 respectively in equation (1), we obtain
A =1, B = −5, and C = 4
Answer - 4 : - Let 
Substituting x = 1, 2, and 3respectively in equation (1), we obtain
Question - 5 : - 
Answer - 5 : - Let 
Substituting x =−1 and −2 in equation (1), we obtain
A =−2 and B = 4
Answer - 6 : -
It can be seen that thegiven integrand is not a proper fraction.
Therefore, on dividing (1− x2) by x(1 − 2x), we obtain
Let 
Substituting x = 0 and 
in equation (1), weobtain
A = 2 and B =3
Substituting in equation(1), we obtain
Question - 7 : - 
Answer - 7 : - Let 
Equating the coefficientsof x2, x, and constant term, we obtain
A + C =0
−A + B =1
−B + C =0
Onsolving these equations, we obtainFrom equation (1), weobtain
Answer - 8 : - Let 
Substituting x =1, we obtain
Equating the coefficientsof x2 and constant term, we obtain
A + C =0
−2A + 2B + C =0
On solving, we obtain
Answer - 9 : - 
Let 
Substituting x =1 in equation (1), we obtain
B = 4
Equating the coefficientsof x2 and x, we obtain
A + C =0
B − 2C =3
Onsolving, we obtain
Answer - 10 : - 
Let 
Equating the coefficientsof x2 and x, we obtain
