Home
Class 12
MATHS
(a) Prove that int(0)^(2x) f(x) dx = 2in...

(a) Prove that `int_(0)^(2x) f(x) dx = 2int_(0)^(2x) f(x) dx` when `f(2a-x) =f(x)` and hence evaluate `int_(0)^(pi) |cos x| dx`.
(b) Prove that `|{:(-a^(2),ab,ac),(bc,-b^(2),bc),(ca,cb,-c^(2)):}|=4a^(2)b^(2)c^(2)`.

Answer

Step by step text solution for (a) Prove that int_(0)^(2x) f(x) dx = 2int_(0)^(2x) f(x) dx when f(2a-x) =f(x) and hence evaluate int_(0)^(pi) |cos x| dx. (b) Prove that |{:(-a^(2),ab,ac),(bc,-b^(2),bc),(ca,cb,-c^(2)):}|=4a^(2)b^(2)c^(2). by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SUPER MODEL QUESTIONS PAPER (WITH ANSWERS)

    SUBHASH PUBLICATION|Exercise PART-D|10 Videos

  • SUPER MODEL QUESTION PAPER FOR PRACTICE

    SUBHASH PUBLICATION|Exercise PART - E|4 Videos

  • SUPPLEMENTARY EXAM QUESTION PAPER JUNE 2018

    SUBHASH PUBLICATION|Exercise PART E|4 Videos

Similar Questions

Explore conceptually related problems

Prove that int_(0)^(2a) f(x) dx = 2int_(0)^(a) f(x) dx when f(2a -x) = f(x) and hence evaluate int_(0)^(pi) |cos x| dx .

int_(0)^(pi//2) cos 2x dx .

Evaluate int_(0)^(2 pi ) cos^(5) x dx

int_(0)^(pi//4) cos^(2) x dx

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (b) int_(0)^(pi/2) cos^(2) xdx .

Prove that int_(0 )^(a) f (x) dx = int_(0)^(a) f (a -x) dx hence evaluate int_(0)^(pi/2) ( cos^5 x)/( cos^2 x+ sinn ^5 x) dx

(a) Prove that int_(0)^(2a)f(x)dx=2int_(0)^(a)f(x)dx,f(2a-x)=f(x) =0,f(2a-x)=-f(x) and hence evaluate int_(0)^(2pi)cos^(5)xdx . (b) Prove that |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=(a-b)(b-c)(c-a)(a+b+c) .

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (e) int_(0)^(2)xsqrt(2 - x) dx .

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx and hence evaluate int_(0)^(pi//2)(2log sin x-log sin2x)dx .

Prove that int_(-a)^(a) dx = {(2int_(0)^(a) f(x) dx, if f(x) "is even"),(0, if f(x) "is odd"):} and hence evaluate (c) int_(0)^(pi)|cosx|dx .

Home
Profile