Q. 6

# Evaluate the following integrals –

Let

Let us assume

We know and derivative of a constant is 0.

x – 2 = λ(2 × 2x2-1 – 6 – 0) + μ

x – 2 = λ(4x – 6) + μ

x – 2 = 4λx + μ – 6λ

Comparing the coefficient of x on both sides, we get

4λ = 1

Comparing the constant on both sides, we get

μ – 6λ = –2

Hence, we have

Substituting this value in I, we can write the integral as

Let

Now, put 2x2 – 6x + 5 = t

(4x – 6)dx = dt (Differentiating both sides)

Substituting this value in I1, we can write

Recall

Let

We can write

Hence, we can write I2 as

Recall

Substituting I1 and I2 in I, we get

Thus,

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Fundamental Integration Formula59 mins
Integration by Substitution56 mins
Interactive Quiz on Integration by Parts56 mins
Interactive Quiz on Integration by Substitution47 mins
Lecture on Integration by parts55 mins
Lecture on some forms of integration54 mins
Lecture on integration by partial fractions62 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

is equal to

Mathematics - Exemplar

Evaluate the following:

Mathematics - Exemplar

is equal to

Mathematics - Exemplar

Evaluate the following:

Mathematics - Exemplar