Integration Worksheet1 Solution2





In this page integration worksheet1 solution2 we are going to see solution of some practice question from the worksheet of integration.

Question 6

Integrate the following with respect to x ,  1/x⁵

Solution:

1/x⁵ = x^(-5)

The given question exactly matches the formula 

∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c

So now we are going to integrate the given question bu using this formula in the question instead of n we have -5

So we get,     

∫ x^(-5) dx  = x^(-5+1)/(-5+1)

            = x^(-4)/(-4) + C

            = -1/4x^4 + C


Question 7

Integrate the following with respect to x ,   x⁻¹ 

Solution:

    x⁻¹  = 1/x

The given question exactly matches the formula 

∫ 1/x dx = log x + c

So now we are going to integrate the given question bu using this formula in the question instead of n we have 16

So we get,     

∫ 1/x dx  = log x

             = log x + C


Question 8

 Integrate the following with respect to x ,   1/x^(5/2) 

Solution:

1/x^(5/2)  = x^(-5/2)

The given question exactly matches the formula 

∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c

So now we are going to integrate the given question bu using this formula in the question instead of n we have -5/2

So we get,     

∫ x^(-5/2) dx  = x^[(-5/2)+1)]/((-5/2)+1))

            = x^(-3/2)/(-3/2) + C

            = (-2/3)x^(-3/2) + C

            = -2/3x^(3/2) + C

            = -2/3x√x + C


Question 9

 Integrate the following with respect to x ,  1/∛x⁵

Solution:

1/∛x⁵  = 1/x^5^(1/3)

           = x^(-5/3)

The given question exactly matches the formula 

∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c

So now we are going to integrate the given question bu using this formula in the question instead of n we have -5/3

So we get,     

∫ x^(-5/3) dx  = x^[(-5/3)+1)]/[(-5/3) + 1]

            = x^[(-5 + 3)/3]/[(-5 + 3)/3)] + C

            = x^(-2/3)/(-2/3) + C

            = -3/2x^(2/3) + C


Question 10

 Integrate the following with respect to x ,(1/x³)^(1/4)

Solution:

  (1/x³)^(1/4) = 1/x^3^(1/4)

                    = 1/x^(3/4)

                    = x^(-1)(3/4)

                    = x^(-3/4)

The given question exactly matches the formula 

∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c

So now we are going to integrate the given question bu using this formula in the question instead of n we have -3/4

So we get,     

∫ x^(-3/4) dx  = x^[(-3/4)+1)]/[(-3/4) + 1)]

            = x^[(-3 + 4)/4]/[(-3 + 4)/4] + C

            = x^(1/4)/(1/4) + C

            =  4x^(1/4) + C

integration worksheet1 solution2 integration worksheet1 solution2