Evaluate the following integrals ∫ x – 3 2 d x .

It is known that, ∫ x n d x = x n + 1 n + 1 + C , where n is any number other than - 1 and C is a constant. Now, integrate the given expression with respect to x , ∫ x - 3 2 d x = x - 3 2 + 1 - 3 2 + 1 + C = x - 1 2 - 1 2 + C = - 2 x + C

Evaluate the following integrals: ∫ 3 x – 7 + x – 1 d x .

It is known: ∫ x n d x = x n + 1 n + 1 + c and ∫ x - 1 d x = ln x Given, ∫ 3 x – 7 + x – 1 d x = ∫ 3 x – 7 d x + ∫ x – 1 d x = 3 ∫ x – 7 d x + ∫ x – 1 d x = 3 x – 7 + 1 – 7 + 1 + ln x + c = – x – 6 2 + log e x + c

Evaluate the following integrals ∫ x + 1 x 2 d x

It is known that ∫ x n d x = x n + 1 n + 1 + C , where n is any number other than - 1 and C is a constant. Now, ∫ x + 1 x 2 d x = ∫ x 2 + 1 x 2 + 2 × x × 1 x d x = ∫ x + 1 x + 2 d x = ∫ x d x + ∫ 1 x d x + 2 ∫ d x = x 2 2 + ln x + 2 x + C

Evaluate the following integrals ∫ x + 1 x d x

It is known that ∫ x n d x = x n + 1 n + 1 + C , where n is any number other than - 1 and C is a constant. And ∫ 1 x d x = log e x Now, integrate the given expression with respect to x . ∫ x + 1 x d x = ∫ x d x + ∫ 1 x d x = ∫ x 1 + 1 1 + 1 + log e x + C = x 2 2 + log e x + C

Evaluate each of the following integrals: ∫ a x 2 + b x + c d x

Given expressions: ∫ a x 2 + b x + c d x As we, know that ∫ x n d x = x n + 1 n + 1 + C Comparing above expressions, then = ∫ a x 2 + b x + c d x = ∫ a x 2 d x + ∫ b x d x + ∫ c d x = a x 2 + 1 2 + 1 + b x 1 + 1 1 + 1 + c x + C = a x 3 3 + b x 2 2 + c x + C = a x 3 3 + b x 2 2 + c x + C

E M B I B E

Beta Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>BEGINNER'S BOX - 11

Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 11: BEGINNER'S BOX - 11

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Embibe Experts Physics Solutions for Exercise - Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 11: BEGINNER'S BOX - 11

Attempt the practice questions on Chapter 2: Mathematical Tools in Physics, Exercise 11: BEGINNER'S BOX - 11 with hints and solutions to strengthen your understanding. Beta Question Bank for Medical: Physics solutions are prepared by Experienced Embibe Experts.