Answer :

Let

Using property

Add (i) and (ii)

We know that cos 2x = 1 – 2sin^{2}x

Divide by cos^{2}x in numerator and denominator

We know that 1 + tan^{2}x = sec^{2}x

Let tan x = t

The limits will also change

When

and

So, the limits will be -1 to 1

Now,

⇒ sec^{2}x dx = dt

Hence

We know that

Hence

**OR**

Here f(x) = 3x^{2} – 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(a^{2} + 2arh + r^{2}h^{2}) – 2a – 2rh + 4

⇒ f(a + rh) = 3a^{2} + 6arh + 3r^{2}h^{2} – 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

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<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