Question

• What applications can you find either in your program of study or elsewhere that require integration to reach a solution?
• How do we recognize an integral whose solution will be a logarithmic form? How do we solve such an integral?

Answer 1

We require integration for finding area of bounded curves, volume of solids, etc. We also apply integration to various physics questions.

The integral whose solutions are in logarithmic form, are in 1/x , 1/(ax + b) forms.

Integral of e^x = e^x

Integral of e^{(ax + b)} = a e^{(ax + b)}

Basic trigonometric integration formulas are used to integrate more complex trigonometric frunctions. There are enormous cases for this, i'm showing you one of them to help you understand this.

Suppose we are asked to integrate sin⁴x cos³x dx

We know the integration of sinx = -cosx and integration of cos x = sinx.

So, for the integral of sin⁴x cos³x dx, we will substitute

sin x as t.

so that, cos x dx = dt