Integration Worksheet2 Solution8

In this page integration worksheet2 solution8 we are going to see solution of some practice question from the worksheet of integration.

Question 8

(i) Integrate the following with respect to x ,e^(3x)

Solution:

The given question exactly matches the formula 

∫  e^(a x) =  (1/a) e^ (a x) + 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,     

∫e^(3 x) dx  = (1/3) e ^(3 x) + C


(ii) Integrate the following with respect to x ,e^(x + 3)

Solution:

The given question exactly matches the formula 

∫  e^(a x + b) =  (1/a) e^ (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,     

∫e^(x + 3) dx  = (1/1) e ^(x + 3) + C

                    = e ^(x + 3) + C     

(iii) Integrate the following with respect to x , e^(3 x + 2)

Solution:

The given question exactly matches the formula 

∫  e^(a x + b) =  (1/a) e^ (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,     

∫ e^(3 x + 2)) dx  = (1/3) e ^(3 x + 2) + C

                    = e ^(3 x + 2)/3 + C     


(iv) Integrate the following with respect to x ,e^(5 - 4 x)

Solution:

The given question exactly matches the formula 

∫  e^(a x + b) =  (1/a) e^ (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,     

∫e^(5 - 4 x) dx  = (1/-4) e ^(5 - 4 x) + C

                    = -e ^(x + 3)/4 + C     


(v) Integrate the following with respect to x ,e^(a x + b)

Solution:

The given question exactly matches the formula 

∫  e^(a x + b) =  (1/a) e^ (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 a

So we get,     

∫e^(a x + b) dx  = (1/a) e ^(a x + b) + C

integration worksheet2 solution8 integration worksheet2 solution8