Integration Worksheet2 Solution6





In this page integration worksheet2 solution6 we are going to see solution of some practice question from the worksheet of integration.

Question 6

(i) Integrate the following with respect to x , sec (3 + x) tan (3 + x)

Solution:

The given question exactly matches the formula 

∫sec (a x + b) tan (a x +b) = (1/a) sec (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,     

∫ sec (3 + x) tan (3 + x) dx  = (1/1) sec (3 -x) + C

                       = sec (3 - x) + C


(ii) Integrate the following with respect to x ,  sec (3 x + 4) tan (3 x + 4)

Solution:

The given question exactly matches the formula 

∫sec (a x + b) tan (a x +b) = (1/a) sec (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 3

So we get,     

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

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


(iii) Integrate the following with respect to x , sec (4 - x) tan (4 - x)

Solution:

The given question exactly matches the formula 

∫sec (a x + b) tan (a x +b) = (1/a) sec (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,     

∫ sec (4 - x) tan (4 - x) dx = (1/-1) sec (4 - x) + C

                                       = - sec (4 - x) + C


(iv) Integrate the following with respect to x , sec (4 - 3 x) tan (4 - 3 x)

Solution:

The given question exactly matches the formula 

∫sec (a x + b) tan (a x +b) = (1/a) sec (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 -3

So we get,     

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

                                       = - sec (4 - 3 x)/3 + C


(v) Integrate the following with respect to x , sec (a x + b) tan (a x + b)

Solution:

The given question exactly matches the formula 

∫sec (a x + b) tan (a x +b) = (1/a) sec (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

So we get,     

∫sec (a x + b) tan (a x + b) dx = (1/a) sec (a x + b) + C

integration worksheet2 solution6 integration worksheet2 solution6