⋆ Pattern – 5
⋆ Pattern : 4
∫
⋆ Pattern – 3 : – Adjustment
1)
⋆ Pattern – 2 :
If ∫f(x) dx = F(x) +c, then
∫ f (a + b) dx = F ( ax + b )dx + c : a ≠ 0
⋆ Pattern – 1
Definite integration never contains any arbitrary constant.
i.e. If = F(x) + c, then
= F(b) – F(a)
Proof :
Now, dx = F(b) – F(a)
= [ F(b) + c ] – [ F(a) + c ]
Examples :
1 If xexy – y = sin2x. Differentiating both the sides with respect to x.
Soln.
Examples :–
1 Evaluate .
01. Introduction
02….
02. Surd
F ( ax + b )dx + c : a ≠ 0
