4. INTRODUCTION
The following trignometric substitutions will be used to handle
integers involving the indicated radicals:
• √x2 + a2 , put x=atanθ
• √ a2 - x2 , put x=asinθ
• √x2 - a2 , put x=asecθ
In case where the above substitutions lead to complicated
integrals, it is sometimes convenient to make the hyperbolic
substitutions.
• x=asinh z for integrals involving √x2 + a2
• x=acosh z for integrals involving √x2 - a2
16. INTRODUCTION
We can use
substitution and
trigonometric identities
to find integral of
certain types of
trigonometric
functions.We begin by
giving the
antiderivatives of the
six basic trigonometric
functions:
17. Example 01:
In this section , will find the Reduction Formula for these intergral
Let we have I = ∫ sinn x dx
I = ∫sin x sinn-1 x dx
By using Integration of parts we have,