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8 months ago

Maths Integrals Class 12th

Kindly Consider the following

7. $\int x^{2} (1 - \frac{1}{x^{2}}) d x$

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Vishal Baghel

Contributor-Level 10

$\begin{array}{l} \int x^{2} - \frac{x^{2}}{x^{2}} d x \\ = \int x^{2} - 1 d x = \int x^{2} d x - \int 1 d x \end{array}$

$= \frac{x^{3}}{3} - x + C$

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New answer posted

8 months ago

Maths Integrals Class 12th

Find the following integrals in Exercises 6 to 20:

6. $\int (4 e^{3 x} + 1) d x$

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Vishal Baghel

Contributor-Level 10

= $\begin{array}{l} \int 4 e^{3 x} d x + \int 1 d x \\ \frac{4 \cdot e^{3 x}}{3} + x + C \end{array}$

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New answer posted

8 months ago

Maths Integrals Class 12th

Kindly Consider the following

5. $s i n 2 x - 4 e 3 x$

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Vishal Baghel

Contributor-Level 10

$\frac{d}{d x} (- \frac{1}{2} c o s 2 x - \frac{4}{3} e^{3 x}) = s i n 2 x - 4 e^{3 x}$

Therefore, an anti-derivative of $(s i n 2 x - 4 e^{3 x}) i s - \frac{1}{2} c o s 2 x - \frac{4}{3} e^{3 x}$

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New answer posted

8 months ago

Maths Integrals Class 12th

Kindly Consider the following

4. ${(a x + b)}^{2}$

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Vishal Baghel

Contributor-Level 10

$d x {(a x + b)}^{3} = 3 a {(a x + b)}^{2}$

${(a x + b)}^{2} = \frac{1}{3 a} . \frac{a}{d x} {(a x + b)}^{3}$

${(a x + b)}^{2} = \frac{d}{d x} (\frac{1}{3 a} {(a x + b)}^{3})$

Therefore, an anti-derivative of ${(a x + b)}^{3} i s \frac{1}{3 a} (a x + b)^{3}$

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New answer posted

8 months ago

Maths Integrals Class 12th

Kindly Consider the following

3. $e^{2 x}$

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Vishal Baghel

Contributor-Level 10

$\begin{array}{l} \frac{d}{d x} (e^{2} x) = 2 e^{2 x} \\ e^{2 x} = \frac{1}{2} - \frac{d}{d x} (e^{2 x}) \\ e^{2 x} = \frac{d}{d x} (\frac{1}{2} e^{2 x}) \end{array}$

Therefore, an anti-derivative of $e^{2 x} i s \frac{1}{2} e^{2 x}$

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New answer posted

8 months ago

Maths Integrals Class 12th

Kindly Consider the following

2. $c o s 3 x$

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Vishal Baghel

Contributor-Level 10

$\begin{array}{l} d x s i n 3 x = 3 c o s 3 x \\ c o s 3 x = \frac{1}{3} d x (s i n 3 x) \\ c o s 3 x = \frac{d}{d x} (\frac{1}{3} s i n 3 x) \end{array}$

Therefore, an anti-derivative of $c o s 3 x i s \frac{1}{3} s i n 3 x$

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New answer posted

8 months ago

Maths Integrals Class 12th

ind an anti-derivative (or integral) of the following functions by the method of inspection.

1. $s i n 2 x$

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Vishal Baghel

Contributor-Level 10

$\begin{array}{l} \frac{d}{d x} c o s 2 x = - 2 s i n 2 x \\ s i n 2 x = - \frac{1}{2} \frac{d}{d x} (c o s 2 x) \\ s i n 2 x = \frac{d}{d x} (\frac{1}{2} c o s 2 x) \end{array}$

Therefore, an anti-derivative of $s i n 2 x i s - \frac{1}{2} c o s 2 x$

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New answer posted

2 years ago

Maths Integrals Cochin University of Science and Technology, Kochi

How to take admission in Integrated BSc MSc Physics at CUSAT?

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Bhukya Sharath Naik

Contributor-Level 10

To take admission in Integrated B.Sc and M.Sc Physics at CUSAT, you need to follow these steps:

Visit the CUSAT admissions website and register for an account.
Fill out the online application form FOR ADMISSION and pay the required application fee.
Upload all the required documents, such as your academic transcripts, entrance exam scorecard, and passport size photographs.
Submit the application form and wait for the results, be careful while uploading

CUSAT selects students for the Integrated B.Sc and M.Sc Physics programme based on their performance in the CUSAT Common Admission Test (CAT). The CAT is a computer-based ent

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