Integration Worksheet1 Solution1





In this page integration worksheet1 solution1 we are going to see solution of some practice question from the worksheet of integration.

Question 1

Integrate the following with respect to x ,  x¹⁶

Solution:

The given question exactly matches the formula 

∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c

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,     

∫ x¹⁶ dx  = x^(16+1)/(16+1)

            = (x^17/17) + C


Question 2

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

Solution:

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^[(5 + 2)/2]/[(5+2)/2]

                   = x^[7/2]/[7/2]

                   = (2/7)x^(7/2) + C


Question 3

Integrate the following with respect to x ,  √x⁷

Solution:

  √x⁷ = x^7^(1/2)

        = x^(7/2)

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 7/2

So we get,     

∫ x^(7/2) dx  = x^[(7/2)+1]/[(7/2) + 1]

                   = x^[(7 + 2)/2]/[(7+2)/2]

                   = x^[9/2]/[9/2]

                   = (2/9)x^(9/2) + C


Question 4:

Integrate the following with respect to x ,   ∛x⁴

Solution:

  ∛x⁴ = x^4^(1/3)

        = x^(4/3)

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 4/3

So we get,     

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

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

                   = x^[7/3]/[7/3]

                   = (3/7)x^(7/3) + C


Question 5:

Integrate the following with respect to x ,   (x^10)^(1/7)

Solution:

  (x^10)^(1/7) = x^(10/7)

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 10/7

So we get,     

∫ x^(10/7) dx  = x^[(10/7)+1]/[(10/7) + 1]

                   = x^[(10 + 7)/7]/[(10+7)/7]

                   = x^[17/7]/[17/7]

                   = (7/17)x^(17/7) + C

integration worksheet1 solution1 integration worksheet1 solution1