Integration Worksheet2 Solution5





In this page integration worksheet2 solution5 we are going to see solution of some practice question from the worksheet of integration.

Question 5

(i) Integrate the following with respect to x ,sec² (2 - x)

Solution:

The given question exactly matches the formula 

sec² (a x + b) =  (1/a) tan (a x + b) + C

Now we are going to integrate the given question by using this formula in the question instead of "a" we have -1

So we get,     

∫ sec² (2 - x) dx  = (1/-1)  tan (2 - x) + C

                          = - tan (2 - x) + C


(ii) Integrate the following with respect to x ,cosec² (5 + 2 x)

Solution:

The given question exactly matches the formula 

cosec² (a x + b) =  -(1/a)  cot (a x + b) + C

Now we are going to integrate the given question by using this formula in the question instead of "a" we have 2

So we get,     

∫ cosec² (5 + 2 x) dx  = -(1/2)  cot (5 + 2 x) + C

                                 = - cot (5 + 2 x)/2 + C


(iii) Integrate the following with respect to x ,Sec² (3 + 4 x)

Solution:

The given question exactly matches the formula 

sec² (a x + b) = (1/a) tan (a x + b) + C

Now we are going to integrate the given question by using this formula in the question instead of "a" we have 4

So we get,     

∫ Sec² (3 + 4 x) dx  = (1/4)  tan (3 + 4 x) + C

                              = tan (3 + 4 x)/4 + C


(iv) Integrate the following with respect to x , cosec² (7 - 11 x)

Solution:

The given question exactly matches the formula 

cosec² (a x + b) = - (1/a) cot (a x + b) + C

Now we are going to integrate the given question by using this formula in the question instead of "a" we have -11

So we get,     

∫ cosec² (7 - 11 x) dx  = -(1/-11)  cot  (7 - 11 x) + C

                              = cot (7 - 11 x)/11 + C


(v) Integrate the following with respect to x ,sec² (p - q x)

Solution:

The given question exactly matches the formula 

sec² (a x + b) = (1/a) tan (a x + b) + C

Now we are going to integrate the given question by using this formula in the question instead of "a" we have -q

So we get,     

∫ sec² (p - q x) dx  = (1/-q)  tan (p - q x) + C

                              = - tan (p - q x)/q + C

integration worksheet2 solution5 integration worksheet2 solution5