Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 400 off


find the area bound by curves y=ex , y=lnx,its assumtodes and the curve x2+y2-2x-2y+1=0 .

6 years ago


Answers : (1)


We need to find the area of the region common to following five curves:

y = e^x

y = lnx

y = 0

x = 0

(x-1)^2+ (y-1)^2 = 1

From the diagram, it is clear that tha area of region ‘A’ is:

A = \int_{0}^{1}1-\sqrt{1-(x-1)^{2}}dx

A = (x-(\frac{(x-1)}{2}.\sqrt{1-(x-1)^{2}}+\frac{1}{2}.sin^{-1}(x-1)))_{0}^{1}

A = 1- \frac{\pi }{4}

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

2 years ago

Post Your Answer

Other Related Questions on Integral Calculus

Intrigate (1÷logx)-(1÷(logx)^2) upper limit e lower limit 2
U could easily break the integration in two parts ; when u would integrate this by using part function(Taking 1 as 2 nd function) , it will get cancelled(other part) and u would end up with ...
2017 years ago
Can any one please tell me the integeration of tanx×tan(x-a)
tan(a) = (tanx – tan(x – a))/(1 + tanx*tan(x-a)) tanx/tana – tan(x – a)/tana – 1 = tanx*tan(x-a) Now see u can easily integerate L.HS. as tana remains as aconstant. Use by part wih tanx and ...
Vikas TU 3 months ago
Sir can you tell the solution of this challenging question? The answer given is ln 8
When you change the 8z part to some y(say), integral should come like ln(8x). I got the formula from wiki. I’m sending yu the page...
KAPIL MANDAL one month ago
I think you are talking about Please check your question. This above integral has the value of ln 8. If you get back on this I can help you with the proof
mycroft holmes one month ago
This uses a technique called Differentiating under the integral sign. Consider the generalized problem of finding the integral This is a function of a. Now differentiating w.r.t a on both...
mycroft holmes one month ago
If 2a+b+2c=0, then the family of lines ax+by+c=0 is concurrent at
Make ax+by+c=0 similar to 2a + b + 2c = 0 therfore multiply ax+by+c=0 by 2 .i.e. 2ax + 2by + 2c = 0 Now compare it with the coeff. of 2a+b+2c=0 we get, x = 1 y = ½ thus at this point it is...
Vikas TU 2 months ago
if tanA = -(tanB)/2 = -1/3 then find A in terms of pi.
if tanA = -(tanB)/2 = -1/3 Given tanA = -1/3 A = arctan(-1/3) => -0.321 radian And tanB = 2/3 B = arctan(2/3) = > 0.588 radian
Vikas TU 2 months ago
Pl provide soln to the attached image!!
a n = Limit x 2 *(f(a n-1 /x) – f(0)) 2 , a n /a n-1 2 = Limit [ [ f(a n-1 /x) – f(0) ]/[ a n-1 /x – 0] ] 2 a n /x will be tendind to 0 as x tends to inf. hence RHS = f’(0) 2 So, an/an-1^2...
Akshay one year ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 400 off

More Questions On Integral Calculus

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details