Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Find $\int \cos 6 x \sqrt{1+\sin 6 x} d x$ 
✓

Answer

Put t = 1 + sin 6x, so that dt = 6 cos 6x dx
Therefore $\int \cos 6 x \sqrt{1+\sin 6 x} d x$ = $\frac{1}{6} \int t^{\frac{1}{2}} d t$ 
= $\frac{1}{6} \times \frac{2}{3}(t)^{\frac{3}{2}}+\mathrm{C}=\frac{1}{9}(1+\sin 6 x)^{\frac{3}{2}}+\mathrm{C}$ 

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 "1 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

Find the angle between the planes $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=5$ and $\vec{r} \cdot(\hat{i}-\hat{j}+\hat{k})=6$.
→
Classify the following measures as scalars and vectors.
10 kg.
→
Write the degree of the differrntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=\text{x}\sin\Big(\frac{\text{dy}}{\text{dx}}\Big).$ 
→
Find the following integrals in Exercises:

$\int\sec\text{x}(\sec\text{x}+\tan\text{x})\text{ dx}$

 

→
Let $\text{A} = \begin{bmatrix}2&4\\3&2\end{bmatrix}, \text{B} = \begin{bmatrix}1&3\\-2&5\end{bmatrix},\text{C} = \begin{bmatrix}-2&5\\3&4\end{bmatrix}.$Find each of the following:
$\text{BA}$
→
If a line has direction ratios 2, –1, –2, then what are its direction cosines?
→
An unbiased die is thrown twice. Let the event A be odd number on the first throw and B the event odd number on the second throw. Check the independence of the events A and B.
→
Find the value of $\tan^{-1}\sqrt{3}-\cot^{-1}(-\sqrt{3}).$
→
If $\text{A}[\text{a}_{\text{ij}}]=\begin{bmatrix}2&3&-5\\1&4&9\\0&7&-2\end{bmatrix}$ and $\text{B}=[\text{b}_\text{ij}]=\begin{bmatrix}2&-1\\-3&4\\1&-2\end{bmatrix}$
Then find a22 + b21
→
Is the function f defined by 
$f(x)=\left\{\begin{array}{ll} {x,} & {\text { if } x \leq 1} \\ {5,} & {\text { if } x>1} \end{array}\right.$  
continuous at x = 0? At x = 1? At x = 2?
→