Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
Evaluate the following integrals:
$\int\Big\{3\sin\text{x}-4\cos\text{x}+\frac{5}{\cos^2\text{x}}-\frac{6}{\sin^2\text{x}}+\tan^2\text{x}-\cot^2\text{x}\Big\}\text{dx}$
✓

Answer

$\int\Big\{3\sin\text{x}-4\cos\text{x}+\frac{5}{\cos^2\text{x}}-\frac{6}{\sin^2\text{x}}+\tan^2\text{x}-\cot^2\text{x}\Big\}\text{dx}$
$=3\int\sin\text{x dx}-4\int\cos\text{x dx}+5\int\sec^2\text{dx}\\-6\int\text{cosec}^2\text{x}+\int\tan^2\text{x dx}-\int\cot^2\text{x dx}$
$=3\int\sin\text{x dx}-4\int\cos\text{x dx}+5\int\sec^2\text{x dx}\\-6\int\text{cosec}^2\text{x}+\int(\sec^2\text{x}-1)\text{dx}-\int(\text{cosec}^2\text{x}-1)\text{dx}$
$=3\int\sin\text{x dx}-4\int\cos\text{x dx}+6\int\sec^2\text{x dx}-7\int\text{cosec}^2\text{x dx}$
$=-3\cos\text{x}-4\sin\text{x}+6\tan\text{x}+7\cot\text{x}+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If two events A and B are such that $\text{P}(\overline{\text{A}})=0.3,\text{P(B)}=0.4$ and $\text{P}(\text{A}\cap\overline{\text{B}})=0.5$ find $\text{P}\Big(\frac{\text{B}}{\overline{\text{A}}\cap\overline{\text{B}}}\Big).$
→
Let * be a binary operation on N given by a * b = LCM (a, b) for all $\text{a, b}\in\text{N.}$ Find 5 * 7.
→
6 boys and 6 girls sit in a row at random. Find the probability that all the girls sit together.
→
Find $x, y, z$ in $\left[\begin{array}{cc}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$
→
An unbiased die with face marked 1, 2, 3, 4, 5, 6 is rolled four times. Out of 4 face values obtained, find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5.
→
If A and B are two events write the expression for the probability of occurrence of exactly one of two events.
→
If f : R → R is defined by f(x) = 10x - 7, then write f-1(x).
→
$\int\sin^2\frac{\text{x}}{2}\text{dx}$
→
Define an associative binary operation on a set.
→
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that.
Both are kings.
→