Question

D. sec2xtanz if y=x" where n is any possitive integer.
​

Answer 1

Answer:

I

n

=∫

cosx

sin(nx)

dx

I

n−2

=∫

cosx

sin(n−2)

dx

I

n

+I

n−2

=∫

cosx

sin[nx]

dx+∫

cosx

sin[(n−2)x

dx

Use sin(A+B)+sin(A−B)=2sinAcosB

∴I

n

+I

n−2

=∫

cos x

2 sin(n−1)x cos x

dx

=2∫sin(n−1)x dx=

n−1

−2

cos(n−1)x+c

⇒I

n

+I

n−2

=

(n−1)

−2

cos(n−1)x+c

Answer 2

Answer:

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Step-by-step explanation:

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