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Question 1: By the method of inspection obtain an integral (or anti - derivative) of the sin 3x. Answer: As the derivative is sin 3xand xis the function of the anti - derivative of sin 3x. i x ( cos 3x) =- 3sin 3x sin 3x =- ½ i x ( cos 3x) sin 3x = i x (-½cos 3x) Hence, the anti-derivative of sin 3x is (-½cos 3x) Question 2: By the method of inspection obtain an integral (or anti - derivative) of the cos 2x. Answer: As the derivative is cos 2xand xis the function of the anti - derivative of cos 2x (sin 2x) =-2cos 2x cos 2x =½i x (sin 2x) cos 2x = i x (-½ ( sin 2x)) Hence, the anti-derivative of sin 2x is (-½cos 2x) Question 3: By the method of inspection obtain an integral (or anti - derivative) of the e 5x _ Answer: As the derivative is e 5x and xis the function of the anti - derivative of e 5x ( e 5 x) = S e 5 x e 5x = (e 5x ) 5 dx e 5 x = ( e 5 x) dx 5 Hence, the anti-derivative of e 5x is½e 5x Question 4: By the method of inspection obtain an integral (or anti - derivative) of the (mx+ n) 2 . Answer: As the derivative is (mx+ n) 2 and xis the function of the anti - derivative of (mx+ n) 2 (mx + n) 3 = 3m(mx + n) 2 (mx + n) 2 = 3 � i x (mx + n) 3 (mx+n) 2 = ( 3 �(mx+n) 3 ) NCERT SOLUTIONS CLASS 12 MATHS CHAPTER-7 EXERCISE-7.1 myncertsolutions.com
