Example 11
![](imgex11.gif)
Solution :
![](imgex11sol1.gif)
![](imgex11sol2.gif)
Example 12
![](imgex12.gif)
Solution : By actual division, i.e.
![](imgex12sol1.gif)
then expressing ![](imgex12sol2.gif)
![](imgex12sol3.gif)
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
![](imgex13sol1.gif)
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
![](imgex13sol2.gif)
\ f (x) = x3 + 2 x2 + 3x + 1
Example 14
Integrate w. r. to x, imgex14.gif
Solution : By actual division
![](imgex14sol1.gif)
![](imgex14sol2.gif)
Example 15
Evaluate ![](imgex15.gif)
Solution : ![](imgex15sol1.gif)
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