Integration Worksheet2 Solution7





In this page integration worksheet2 solution7 we are going to see solution of some practice question from the worksheet of integration.

Question 7

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

Solution:

The given question exactly matches the formula 

∫ cosec (a x + b) cot (a x + b) =  - (1/a) cosec (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,     

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

                                          = cosec (2 - x) + C


(ii) Integrate the following with respect to x ,cosec (4 x + 2) cot (4 x + 2)

Solution:

The given question exactly matches the formula 

∫ cosec (a x + b) cot (a x + b) =  - (1/a) cosec (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,     

∫cosec (4 x + 2) cot (4 x + 2) dx  = -(1/4) cosec (4 x + 2) + C

                                                 = -cosec (4 x + 2)/4 + C


(iv) Integrate the following with respect to x ,cosec (3 - 2 x) cot (3 - 2 x)

Solution:

The given question exactly matches the formula 

∫ cosec (a x + b) cot (a x + b) =  - (1/a) cosec (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,     

∫cosec (3 - 2 x) cot (3 - 2 x) dx  = -(1/-2) cosec (3 - 2 x) + C

                                               = cosec (3 - 2 x)/2 + C


(iv) Integrate the following with respect to x , cosec (L x + m) cot (L x + m)

Solution:

The given question exactly matches the formula 

∫ cosec (a x + b) cot (a x + b) =  - (1/a) cosec (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 L

So we get,     

∫cosec (L x + m) cot (L x + m) dx  = -(1/L) cosec (L x + m) + C

                                                   = - cosec (L x + m)/L + C

integration worksheet2 solution7 integration worksheet2 solution7