Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.7,Q.11,Page 330

Question

$\int {\sqrt {{x^2} - 8x + 7} dx}$ is equal to

(a) $\cfrac{1}{2}\left( {x - 4} \right)\sqrt {{x^2} - 8x + 7} + 9\log \left| {x - 4 + \sqrt {{x^2} - 8x + 7} } \right| + C$
(b) $\cfrac{1}{2}\left( {x + 4} \right)\sqrt {{x^2} - 8x + 7} + 9\log \left| {x + 4 + \sqrt {{x^2} - 8x + 7} } \right| + C$
(c) $\cfrac{1}{2}\left( {x - 4} \right)\sqrt {{x^2} - 8x + 7} - 3\sqrt 2 \log \left| {x - 4 + \sqrt {{x^2} - 8x + 7} } \right| + C$
(d) $\cfrac{1}{2}\left( {x - 4} \right)\sqrt {{x^2} - 8x + 7} - \cfrac{9}{4}\log \left| {x - 4 + \sqrt {{x^2} - 8x + 7} } \right| + C$

Step-by-step Solution

Option d is correct

Let $I = \int {\sqrt {{x^2} - 8x + 7} dx} = \int {\sqrt {{{\left( {x - 4} \right)}^2} - {3^2}} } dx$

$= \cfrac{{x - 4}}{2}\sqrt {{x^2} - 8x + 7} - \cfrac{9}{2}\log \left| {\left( {x - 4} \right) + \sqrt {{x^2} - 8x + 7} } \right| + C$

$figure$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.