NCERT SOLUTIONS CLASS 12 MATHS APTER-7 EXERCISE-7.1 ... · Integral of au2 + eu and u is the...
Transcript of NCERT SOLUTIONS CLASS 12 MATHS APTER-7 EXERCISE-7.1 ... · Integral of au2 + eu and u is the...
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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 3x and x is the function of the anti - derivative of sin 3x.
ix
( cos 3x) =- 3sin 3x
sin 3x =- ½ ix
( cos 3x)
sin 3x = ix
(-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 2x and x is the function of the anti - derivative of cos 2x
:fx (sin 2x) =-2cos 2x
cos 2x =½ix
(sin 2x)
cos 2x = ix
(-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 e5x _
Answer:
As the derivative is e5x and x is the function of the anti - derivative of e5x
:fx ( e5x) = Se5x
e5x = .! ..!i._ (e5x )
5 dx
e5x = ..!i_ ( .!.e5x)
dx 5
Hence, the anti-derivative of e5xis½e5x
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
:fx (mx + n)3 = 3m(mx + n)2
(mx + n)2
= 3� ix (mx + n)3
(mx+n)2 = :fx(
3�(mx+n)3 )
NCERT SOLUTIONS CLASS 12 MATHS
CHAPTER-7 EXERCISE-7.1
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