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Example 11

Solution :

Example 12

Solution : By actual division, i.e.

then expressing

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Example 13

Given that f’ (x) = 3x2 + 4x + a, f ( 0) = 1 and f (2) = 11 Find f(x)

Solution : On integrating w.r. to x, the given relation, we get

Now f (0) = 1 gives f (0) = (0)3 + 2 (0)2 + a (0) + c = 1

i. e. c = 1.

Also, f (2) = 11 gives, f (2) = (2)3 + 2 (2)2 + a (2) + c = 11

i.e. 8 + 8 + 2a + c = 11

i.e. 2a + c = -5

i.e. 2 a + 1 = -5

i.e. 2a = -6

\ f (x) = x3 + 2 x2 + 3x + 1

Example 14

Integrate w. r. to x, imgex14.gif

Solution : By actual division

Example 15

Evaluate

Solution :

Index

6.1 Anti-derivatives (indefinite Integral)
6.2 Integration Of Some Trignometric Functions
6.3 Methods Of Integration
6.4 Substitution And Change Of Variables
6.5 Some Standard Substitutions
6.6 Integration By Parts
6.7 Integration By Partial Fractions

Chapter 7