_ ^ x^2 - 8x + 7 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\sqrt {{x^2} - 8x + 7} } \;dx = $

A
$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} + 9\log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$
B
$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} - 3\sqrt 2 \log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$
✓
$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} - \frac{9}{2}\log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$
D
None of these

✓

Answer

Correct option: C.

$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} - \frac{9}{2}\log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$

c
(c)$\int_{}^{} {\sqrt {{x^2} - 8x + 7} \,dx = \int_{}^{} {\sqrt {{{(x - 4)}^2} - {{(3)}^2}} \,dx} } $
Now apply formula of $\int_{}^{} {\sqrt {{x^2} - {a^2}} \,dx.} $

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $a = min\,\, [x^2 + 2x + 3, x \in R]$ and $b =$ $\mathop {Lim}\limits_{x \to 0} \,\,\frac{{\sin x\cos x}}{{{e^x} - {e^{ - x}}}}$ . Then the value of $\sum\limits_{r = 0}^n {{a^r}{b^{n - r}}} $ is

If $b _{ n }=\int \limits_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} nx }{\sin x } dx , n \in N$, then

If $ P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3) $ and $ S(x_4, y_4) $ are $4 $ concyclic points on the rectangular hyperbola $x y = c^2$ , the co-ordinates of the orthocentre of the triangle $ PQR$ are :

Let the mean and variance of four numbers $3,7, x$ and $y(x>y)$ be $5$ and $10$ respectively. Then the mean of four numbers $3+2 \mathrm{x}, 7+2 \mathrm{y}, \mathrm{x}+\mathrm{y}$ and $x-y$ is ..... .

Let $f(x)$ and $g(x)$ be two functions satisfying $f\left(x^{2}\right)$ $+g(4-x)=4 x^{3}$ and $g(4-x)+g(x)=0$, then the value of $\int_{-4}^{4} f(x)^{2} d x$ is

The least remainder when ${17^{30}}$ is divided by $ 5$ is

$\int_{}^{} {\frac{{dx}}{{{e^x} + {e^{ - x}}}} = } $

Let the centroid of an equilateral triangle $ABC$ be at the origin. Let one of the sides of the equilateral triangle be along the straight line $x + y =3$. If $R$ and $r$ be the radius of circumcircle and incircle respectively of $\Delta ABC ,$ then $( R + r )$ is equal to ..... .

Let $C: x^2+y^2=4$ and $C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $\mathrm{C}$ and $\mathrm{C}^{\prime}$ intersect at two distinct points, is ${R}-[a, b]$, then the point $(8 a+12,16 b-20)$ lies on the curve:

The function $f(x) = \sin \frac{{\pi x}}{2} + 2\cos \frac{{\pi x}}{3} - \tan \frac{{\pi x}}{4}$ is period with period