Match Column I to Column II. (A) If ∫ cos 5 x d x = sin x + sin 3 x / m + sin 5 x / n + C , find n + 2 m . (B) If ∫ x 2 − 8 x + 15 x d x = ln ( x − 3 ) b ( x − 5 ) a + C , find a + b . (C) For

Question

Match Column I to Column II. (A) If ∫ cos 5 x d x = sin x + sin 3 x / m + sin 5 x / n + C , find n + 2 m . (B) If ∫ x 2 − 8 x + 15 x ​ d x = ln ​ ( x − 3 ) b ( x − 5 ) a ​ ​ + C , find a + b . (C) For y = f ( t ) , x = g ( t ) , if f ′ ( 1 ) = 0 , g ′ ( 1 ) = 1 , f ′′ ( 1 ) = 2 , find d 2 y / d x 2 at t = 1 . (D) If L = lim x → 0 + ​ ( − ln x ) 1/ ( x l n x ) , find ln L . Column II: (P) 2, (Q) 3, (R) 0, (S) -2, (T) natural number.

TestHub · Accepted Answer

(A) Expanding ( 1 − sin 2 x ) 2 gives coefficients m = − 3/2 , n = 5 , hence n + 2 m = 2 . (B) Partial fractions give a = 5/2 , b = 3/2 , so the sum is 4, a natural number. (C) The parametric second-derivative formula gives 2. (D) Taking logarithms gives ln L = lim ln ( − ln x ) / ( x ln x ) = 0 .

Mathematics - Indefinite Integration Question with Solution | TestHub

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