# Evaluate the foll

Let

Using property

We know that cos 2x = 1 – 2sin2x

Divide by cos2x in numerator and denominator

We know that 1 + tan2x = sec2x

Let tan x = t

The limits will also change

When

and

So, the limits will be -1 to 1

Now,

sec2x dx = dt

Hence

We know that

Hence

OR

Here f(x) = 3x2 – 2x + 4

Expressing integral as limit of sum

Where

Let us find f (a + rh)

f(a + rh) = 3(a + rh)2 – 2(a + rh) + 4

f(a + rh) = 3(a2 + 2arh + r2h2) – 2a – 2rh + 4

f(a + rh) = 3a2 + 6arh + 3r2h2 – 2a – 2rh + 4

Here a = -2 and b = 2

b – a = 2 – (-2) = 4 and

Put this value of f(a + rh) in (i)

Since ,

And,

Put the limit

As

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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 :

<span lang="EN-USRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2

Evaluate the follRD Sharma - Volume 2