RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.14) Exercise 19.14

Students can use the PDF as a reference guide to help them understand and practice to do well on the Class 12 exam. Working with RD Sharma Solutions regularly helps students enhance their problem-solving and logical thinking skills. This is essential for improving academic results.

Chapter 19 Exercise 19.14: Important Topics from the Chapter RD Sharma Solutions Class 12 Maths

• The following are some of the key themes discussed in RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.14.

• The term antiderivative is defined as Indefinite integral.

• Formulas for basic integration

• Some standard integration findings, as well as the corollary

• Trigonometric functions integration

• Exponential functions' integration

• Problems of many kinds

• Indefinite integral's geometric interpretation

• Differences and similarities between differentiation and integration

• Integration techniques

• Substitutional integration

• Some typical outcomes

• Using trigonometric substitutions to evaluate integrals

• Some unique integrals

• Parts-based integration

• Some key integrals, as well as theorems

• Using partial fractions to integrate rational algebraic functions

• When the denominator can be expressed as a product of linear components

• When there are some repeated linear components in the denominator

• There are irreducible quadratic factors in the denominator.

Ex 19.14 Example 1: Indefinite Integrals

Let     I = \[\int \frac{1}{a^{2}-b^{2}x^{2}}dx\]

             = \[\frac{1}{b^{2} }\int\frac{1}{\frac{a^{2}}{b^{2}}-x^{2}}dx\]

             = \[\frac{1}{b^{2}}\int \frac{1}{(\frac{a}{b})^{2}-x^{2}}dx\]

  I =\[\frac{1}{b^{2} }\times \frac{1}{2\times (\frac{a}{b})}log\left | \frac{\frac{a}{b}+x}{\frac{a}{b}-x} \right |+c\] (\[since\int \frac{1}{a^{2}-x^{2}}dx=\frac{1}{2a}log\left | \frac{x+a}{x-a} \right |+c\])

I = \[\frac{1}{2ab}log\left | \frac{a+bx}{a-bx} \right |+c\]

Hence the article provides important information such as the Important Topics from the Chapter RD Sharma Solutions Class 12 Maths. Students should visit the website of Vedantu and practice questions.