Integration Worksheet2 Solution4

In this page integration worksheet2 solution4 we are going to see solution of some practice question from the worksheet of integration.

Question 4

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

Solution:

The given question exactly matches the formula 

∫sin (a x + b) =  - (1/a) cos (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,     

∫ sin (x + 3) dx  = -(1/1) cos (x + 3) + C

                       = - cos (x + 3) + C


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

Solution:

The given question exactly matches the formula 

∫sin (a x + b) =  - (1/a) cos (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,     

∫ sin (2 x + 4) dx  = -(1/2) cos (2 x + 4) + C

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


(iii) Integrate the following with respect to x ,sin (3 - 4 x)

Solution:

The given question exactly matches the formula 

∫sin (a x + b) =  - (1/a) cos (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,     

∫ sin (3 - 4 x) dx  = -(1/4) cos (3 - 4 x) + C

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


(iv) Integrate the following with respect to x , cos (4 x + 5)

Solution:

The given question exactly matches the formula 

∫cos (a x + b) =  (1/a) sin (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,     

∫ cos (4 x + 5) dx  = (1/4) sin (4 x + 5) + C

                           = sin (4 x + 5)/4 + C


(v) Integrate the following with respect to x ,cos (5 - 2 x)

Solution:

The given question exactly matches the formula 

∫cos (a x + b) =  (1/a) sin (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,     

∫ cos (5 - 2 x) dx  = (1/2) sin (5 - 2 x) + C

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

integration worksheet2 solution4 integration worksheet2 solution4