Download App

Maxima and Minima — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMaxima and Minima3 Marks
Question
Write a value of $\int\tan^6\text{x}\sec^2\text{x}\text{ dx}$
✓

Answer

Let $\text{I}=\int\tan^6\text{x}\sec^2\text{x}\text{ dx}$
Let $\tan\text{x}=\text{t}$
$\sec^2\text{x dx}=\text{dt}$
$\therefore\ \text{I}=\int\text{t}^6\text{dt}$
$=\frac{\text{t}^7}{7}+\text{C}$
Thus, $\text{I}=\frac{\tan^7\text{x}}{7}+\text{C}$

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 "3 Marks Question" from Maxima and Minima→Maxima and Minima — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Check the commutativity and associativity of the following binary operations:
$'*'$ on $Q$ defined by $a * b = ab^2 $ for all $a, b ∈ Q.$
→
Using differentials, find the approximate value of each of the following:
$(33)^{-\frac{1}{5}}$
→
Classify the following functions as injection, surjection or bijection:
$f : R \rightarrow R,$ defined by $f(x) = \sin^2x + \cos^2x$
→
Evaluate the integral: $\sec ^{-1} \sqrt{x} d x$
→
Evaluate the following:
$\int\limits^2_1\frac{\text{dx}}{\sqrt{(\text{x}-1)(2-\text{x})}}$
→
Let f be an invertible real function. Write $\mathrm{(f^{-1}of)(1) + (f^{-1}of)(2) + ..... + (f^{-1}of)(100).}$
→
$\text{If y}=\cos^{-1}\text{x},\text{ Find }\frac{\text{d}^2\text{y}}{\text{dx}^2}\text{ in terms of y alone}.$
→
Evaluate the following integrals:$\int\frac{\sin\text{x}-\cos\text{x}}{\sqrt{\sin2\text{x}}}\text{ dx}$
→
A laboratory blood test is $99 \%$ effective in detecting a certain disease when its infection is present. However, the test also yields a false positive result for $0.5 \%$ of the healthy person tested (i.e. if a healthy person is tested, then, with probability $0.005$ , the test will imply he has the disease). If $0.1 \%$ of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
→
Evaluate the following integrals:
$\int^\limits4_1\text{f(x)}\text{dx},$ Where $\text{f(x)}=\begin{cases}7\text{x}+3,&\text{if }\ 1\leq\text{x}\leq3\\8\text{x},&\text{if }\ 3\leq\text{x}\leq9\end{cases}$
→