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Integration

Theory and Formula


Q1. Integrate the function :
y = ex(cos2x - sin2x)

(a) exsin2x + c (b) cos2x + c (c) ex.cos2x + c (d) ex + c

Solution.
(c) ex.cos2x + c
Solution

Q2. Integrate the function ,
y = ex(1/x - 1/x2)

(a) ex/x + c (b) ex + c (c) 1/x + c (d) xex + c

Solution.
(a) ex/x + c
Solution

Q3. Find ∫
dx/ 3- 6x - x2

Solution.
Solution

Q4. Find ∫
(5 + logx)5/ x
dx =

Solution.
∫
(5 + logx)5/ x
dx = ∫(5 + logx)5 . (
1/x
)dx

(5+logx)6/ 6
+ c
Solution

Q5. Evaluate ∫
x3 - x2 + x - 1/ x-1
dx

Solution.
Let I = ∫
x3 - x2 + x - 1/ x-1
dx

= ∫
x2(x-1) + 1(x-1)/x-1
dx

∫
(x2 + 1)(x-1)/ x-1
dx = ∫(x2 + 1)dx

=
x3 /3
+ x + c
Solution