Home
Class 12
MATHS
If int(e^(x)(1+100x^(99)-x^(200)))/((1-x...

If `int(e^(x)(1+100x^(99)-x^(200)))/((1-x^(100))sqrt(1-x^(200)))dx=e^(x)((1-x^(k))/(1+x^(l)))^(m)+c`, then

A

`k=100 ,m=1`

B

`k=99, m=(1)/(2)`

C

`k=99, m=1`

D

`k=100, m=-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`I= int e^(x)( sqrt((1+x^(100))/(1-x^(100)))+(100x^(99))/((1-x^(100))sqrt(1-x^(200))))dx`
Now `(d)/(dx) (sqrt((1+x^(100))/(1-x^(100))))=(100x^(99))/((1-x^(100))sqrt(1-x^(2000)))`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 8

    VMC MODULES ENGLISH|Exercise MATHMATICS (SECTION 2)|5 Videos

  • MOCK TEST 7

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 9

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx=mu e^(x)((1+x)/(1-x))^(lambda)+C , then 2(lambda+mu) is equal to ..... .

∫ 1 / 2 − 1 int(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))

Evaluate: int(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))

Evaluate: int(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))

int(1+x-x^(- 1))e^(x+x^(-1))dx=

int_((e^x(2-x^2))/((1-x)sqrt(1-x^2))\ dx) is equal to

If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C , then

int(1+x-x^(- 1))e^(x+x^(- 1))dx=

int ((1-x)/(1+x^(2)))^(2) e^(x)dx

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: int(e^x(2-x^2))/((1-x)sqrt(1-x^2))dx (A) e^xsqrt((1-x)/(1+x))+C (B) e^xsqrt((1+x)/(1-x))+C (C) e^xsqrt((2-x)/(2+x))+C (D) none of these