Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\sqrt {1 + \cos x} \;dx} $ equals
  • ✓
    $2\sqrt 2 \sin \frac{x}{2} + c$
  • B
    $ - 2\sqrt 2 \sin \frac{x}{2} + c$
  • C
    $ - 2\sqrt 2 \cos \frac{x}{2} + c$
  • D
    $2\sqrt 2 \cos \frac{x}{2} + c$
✓

Answer

Correct option: A.
$2\sqrt 2 \sin \frac{x}{2} + c$
a
(a) $I = \int_{}^{} {\sqrt {1 + \cos x} \,dx} = \int_{}^{} {\sqrt {2{{\cos }^2}(x/2)} dx} $
$I = \sqrt 2 \int_{}^{} {\cos (x/2\,)dx} = 2\sqrt 2 \sin (x/2) + c$.

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 "M.C.Q (1 Marks)" from 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The general solution of the differential equation $\frac{d y}{d x}+\frac{y}{x}=1$ is
→
What is the length of the longer diagonal of the parallelogram constructed on $5\vec{\text{a}}+2\vec{\text{b}}$ and $\vec{\text{a}}-3\vec{\text{b}}$ if it is given that $|\vec{\text{a}}|=2\sqrt{2},\big|\vec{\text{b}}\big|=3$ and the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\frac{\pi}{4}$?
  1. $15$
  2. $\sqrt{113}$
  3. $\sqrt{593}$
  4. $\sqrt{369}$
→
$a\times [a\times (a\times b)]$ is equal to
→
If the co-ordinates of the points $A, B, C, D$ be $(1, 2, 3), (4, 5, 7), (-4, 3, -6)$ and $(2, 9, 2)$ respectively, then the angle between the lines $AB$ and $CD$ is
→
The angle between the straight lines $\frac{{x - 2}}{2} = \frac{{y - 1}}{5} = \frac{{z + 3}}{{ - 3}}$ and $\frac{{x + 1}}{{ - 1}} = \frac{{y - 4}}{8} = \frac{{z - 5}}{4}$ is
→
The direction cosines of the normal to the plane 2x - 3y - 6z - 3 = 0 are:
→
Choose the correct answer from the given four options.
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is:
  1. ${^5}\text{C}_4(0.7)^4(0.3)$
  2. ${^5}\text{C}_1(0.7)^4(0.3)^4$
  3. ${^5}\text{C}_4(0.7)(0.3)^4$
  4. $(0.7)^4(0.3)$
→
Evaluate: $\int\frac{3\text{x}^2+1}{(\text{x}^2-1)^3}\text{dx}$
  1. $\text{c}-\frac{\text{x}}{(\text{x}^2-1)^2}$
  2. $\text{c}-\frac{\text{x}}{(\text{x}^2+1)^2}$
  3. $\frac{\text{x}}{(\text{x}^2-1)^2}$
  4. $\frac{\text{x}}{(\text{x}^2+1)^2}$
→
Probability that $A$ speaks truth is $\frac{4}{5}.$ A coin is tossed. A reports that a head appears. The probability that actually there was head is
→
The records of a hospital show that $10\%$ of the cases of a certain disease are fatal. If $6$ patients are suffering from the disease, then the probability that only three will die is
→