Evaluate the following integrals: ^ 2 _ - 2 (2 |x|+ |x| )dx - Vidyadip

Question

Evaluate the following integrals:
$\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\big(2\sin|\text{x}|+\cos|\text{x}|\big)\text{dx}$

✓

Answer

$\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\big(2\sin|\text{x}|+\cos|\text{x}|\big)\text{dx}$
$=\int^{0}_{-\frac{\pi}{4}}\big(-2\sin\text{x}+\cos\text{x}\big)\text{dx}+\int_{0}^{\frac{\pi}{2}}\big(2\sin\text{x}+\cos\text{x}\big)\text{dx}$
$=\big[2\cos\text{x}+\sin\text{x}\big]^0_{-\frac{\pi}{4}}+\big[-2\cos\text{x}+\sin\text{x}\big]_0^{\frac{\pi}{2}}$
$=2+0-0+1+0+1+2-0$
$=6$

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 Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Test whether the following relations $R_2$ are:

Reflexive.
Symmetric.
Transitive.

$R_2$ on Z defined by $(\text{a, b})\in\text{R}_2\Leftrightarrow\ |\text{a}-\text{b}|\leq5$

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:
$\text{g}(\text{x})\frac{\text{x}}{2}+\frac{2}{\text{x}},\text{x}\geq0$

If $\text{y}=\text{ax}^{\text{n+1}}+\text{bx}^{-\text{n}}$ and $\text{x}^2\frac{\text{d}^2\text{y}}{\text{dx}^2}=\lambda\text{y}$ then write the value of $\lambda$

Define $\vec{\text{a}}\times\vec{\text{b}}$ and prove that $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\big(\vec{\text{a}}.\vec{\text{b}}\big)\tan\theta,$ where $\theta$ is the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

Find the inverse of the following matrices:$\begin{bmatrix} \text{a} & \text{b} \\ \text{c} & \frac{1+\text{bc}}{\text{a}} \end{bmatrix}$

Given a non-empty set $X,$ let $*: P(X) \times P(X) \rightarrow P(X)$ be defined as $\text{A}*\text{B} =(\text{A – B})\cup(\text{B – A}),\forall\text{A},\text{B}\in\text{P(X)}.$Show that the empty set $\phi$ is the identity for the operation $*$ and all the elements $A$ of $P(X)$ are invertible with $A^{–1} = A. (\text{Hint: }(\text{A}-\phi)\cup(\phi-\text{A})=\text{A}\ \text{and }(\text{A}-\text{A})\cup(\text{A}-\text{A})=\text{A}*\text{A}=\phi).$

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:
$\text{h}\text{(x)}=\sin \text{x}-\cos \text{x}, 0< \text{x}<\frac{\pi}{2}$

Show that the line through the points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (-1, -2, 1) and, (1, 2, 5).

An urn contains 3 white, 4 red and 5 black balls. Two balls are drawn one by one without replacement. What is the probability that at least one ball is black?

Evalute the following integrals:
$\int\frac{10\text{x}^9+10^\text{x}\log_\text{e}10}{10^\text{x}+\text{x}^{10}}\text{dx}$