Integration Worksheet1 Solution3





In this page integration worksheet1 solution3 we are going to see solution of some practice question from the worksheet of integration.

Question 11

Integrate the following with respect to x ,  (1/cosecx)

Solution:

1/cosec x can be written as sin x

∫ Sin x dx = - cos x + c


∫ 1/cosec x dx  =  ∫ sin dx

                     = - cos x + C


Question 12

 Integrate the following with respect to x , tan x/cos x

Solution:

    tan x/cos x = tan x (1/cos x)

                    = tan x sec x

The given question exactly matches the formula 

∫ sec x tan x dx = sec x + c

                     = ∫ tan x sec x dx

                     = sec x + C


Question 13

 Integrate the following with respect to x , cos x/sin²x

Solution:

    cos x/sin²x = cos x/(sin x sin x)

                    = (cos x/sin x) (1/sin x)

                    = cot x cosec x

The given question exactly matches the formula 

cot x cosec x dx = - cosec x + c

                     = ∫ cot x cosec x dx

                     = - cosec x + C

integration worksheet1 solution3 integration worksheet1 solution3


Question 14

 Integrate the following with respect to x , 1/cos²x

Solution:

         1/cos²x = sec²x   

The given question exactly matches the formula 

sec²x dx = tan x + c

                     = ∫sec²x dx

                     = tan x + C


Question 15

Integrate the following with respect to x , 1/e^(-x)

Solution:

1/e^(-x) = e^x

The given question exactly matches the formula 

e^x  dx = e^x + c

                     = ∫e^x dx

                     = e^x + C

integration worksheet1 solution3 integration worksheet1 solution3