Evaluate: intx\ sqrt(1+x-x^2)\ dx...

Evaluate: `intx\ sqrt(1+x-x^2)\ dx`

Text Solution

Verified by Experts

The correct Answer is:

`-(1)/(3)(1+x-x^(2))^(3//2)+1/2 [ ((x-1//2))/(2)sqrt(1+x-x^(2))+5/8 sin^(-1)((2x-1)/(sqrt(5)))]+C`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INDEFINITE INTEGRAL
ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|15 Videos
INDEFINITE INTEGRAL
ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|15 Videos
HYPERBOLA
ARIHANT MATHS ENGLISH|Exercise Hyperbola Exercise 11 : Questions Asked in Previous 13 Years Exams|3 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

Evaluate: intx/(sqrt(8+x-x^2))\ dx

Evaluate: intx^2\ sqrt(a^6-x^6)\ dx

Evaluate: intx^2sqrt(1+x)dx

Evaluate: intx^2\ sqrt(1+x)\ dx

Evaluate: intx^2\ sqrt(x+2)\ dx

Evaluate: intx/(sqrt(x^2+x+1))\ dx

Evaluate: intx/(x-sqrt(x^2-1))\ dx

Evaluate: intx\ sqrt(x+2)\ dx

Evaluate: intx\ sqrt(x+2)\ dx

Evaluate: intx^2sqrt(x+2)dx

ARIHANT MATHS ENGLISH-INDEFINITE INTEGRAL -Exercise (Questions Asked In Previous 13 Years Exam)

Evaluate: intx\ sqrt(1+x-x^2)\ dx
Text Solution
|
The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...
Text Solution
|
If I=int(e^x)/(e^(4x)+e^(2x)+1) dx. J=int(e^(-x))/(e^(-4x)+e^(-2x)+1) ...
Text Solution
|
The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to ...
Text Solution
|
"The integral " int(dx)/(x^(2)(x^(4)+1)^(3//4))" equals"
Text Solution
|
"The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "
Text Solution
|
"If " int f(x)dx=Psi(x), " then " int x^(5)f(x)^(3)dx " is equal to "
Text Solution
|
If the integral int(5tanx)/(tanx-2)dx=x+a"ln"|sinx-2cosx|+k then a is...
Text Solution
|
The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx , is
Text Solution
|