Evaluating Integrals with Substitution

Gamma

Theta

Beta

Alpha

To make it a definite integral

To change the variable

To simplify the calculation

To avoid dealing with complex boundaries

Theta squared

Theta cubed

Theta to the power of four

Theta to the power of half

Cosine inverse

Logarithm

Sine inverse

Tangent inverse

By reverting to original x boundaries

By using arbitrary values

By ignoring them completely

By changing them to theta boundaries

Zero

Pi

Infinity

Negative Pi

It approaches zero

It approaches pi/2

It remains constant

It becomes undefined

Because it is always zero

Because it involves complex numbers

Because it simplifies to a neat result despite unbounded conditions

Because it is undefined

To make the integral undefined

To handle unbounded conditions

To change the variable

To avoid using theta

Cosine inverse

Exponential

Tangent inverse

Sine inverse