Evaluate: ∫√7x-10-x2dx

Question

Evaluate: ∫√7x-10-x2dx (A) (1/4)(2x-7)√7x-10-x2+(9/8)sin-1((2x-7/3 ))+C  (B) -(1/4)(2x-7)√7x-10-x2-(9/8)sin-1((2x-7/3 ))+C  (C) -(1/4)(2x-7)√7x-10-x2+(9/8)sin-1((2x-7/3 ))+C  (D) None of these

Tardigrade Admin · Accepted Answer

I= ∫√-(x2-7x +10)dx I ∫√-(x2-7x+(49/4)-(49/4)+10)dx ⇒ I = ∫√- (x-(7/2))2-((3/2))2 dx = ∫√((3/2))2-(x-(7/2))2dx ⇒ I= (1/2)(x-(7/2))√((3/2))2-(x-(7/2))2 +(1/2)⋅((3/2))2 sin-1((x-((7/2))/(3)2))+C ⇒ I =(1/4)(2x-7)√7x-10-x2+(9/8)sin-1((2x-7/3 ))+C

Q. Evaluate: $\int 7 x - 10 - x^{2} d x$

$\frac{1}{4} (2 x - 7) 7 x - 10 - x^{2} + \frac{9}{8} s i n^{- 1} (\frac{2 x - 7}{3}) + C$

$- \frac{1}{4} (2 x - 7) 7 x - 10 - x^{2} - \frac{9}{8} s i n^{- 1} (\frac{2 x - 7}{3}) + C$

$- \frac{1}{4} (2 x - 7) 7 x - 10 - x^{2} + \frac{9}{8} s i n^{- 1} (\frac{2 x - 7}{3}) + C$

None of these

Q. Evaluate: ∫7x−10−x2​dx

41​(2x−7)7x−10−x2​+89​sin−1(32x−7​)+C

−41​(2x−7)7x−10−x2​−89​sin−1(32x−7​)+C

−41​(2x−7)7x−10−x2​+89​sin−1(32x−7​)+C

None of these

I=∫−(x2−7x+10)​dx I∫−(x2−7x+449​−449​+10)​dx ⇒I=∫−{(x−27​)2−(23​)2}​dx=∫(23​)2−(x−27​)2​dx ⇒I=21​(x−27​)(23​)2−(x−27​)2​+21​⋅(23​)2sin−1(23​x−(27​)​)+C ⇒I=41​(2x−7)7x−10−x2​+89​sin−1(32x−7​)+C

Q. Evaluate: $\int 7 x - 10 - x^{2} d x$

$\frac{1}{4} (2 x - 7) 7 x - 10 - x^{2} + \frac{9}{8} s i n^{- 1} (\frac{2 x - 7}{3}) + C$

$- \frac{1}{4} (2 x - 7) 7 x - 10 - x^{2} - \frac{9}{8} s i n^{- 1} (\frac{2 x - 7}{3}) + C$

$- \frac{1}{4} (2 x - 7) 7 x - 10 - x^{2} + \frac{9}{8} s i n^{- 1} (\frac{2 x - 7}{3}) + C$