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

a) Prove that `int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx" and evaluate "int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx))`
b) Prove that `|{:(1+a^(2)-b^(2), 2ab, -2b), (2ab, 1-a^(2)+b^(2), 2a), (2, -2a, 1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3)`

Answer

Step by step text solution for a) Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx" and evaluate "int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) b) Prove that |{:(1+a^(2)-b^(2), 2ab, -2b), (2ab, 1-a^(2)+b^(2), 2a), (2, -2a, 1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3) 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

  • II PUC MATHEMATICS P.U. BOARD LATEST MODEL QUESTION PAPER - 1

    SUNSTAR PUBLICATION|Exercise PART - D|9 Videos

  • II PUC MATHEMATICS ANNUAL EXAM QUESTION PEPER MARCH -17

    SUNSTAR PUBLICATION|Exercise PART -D|12 Videos

  • II PUC MATHEMATICS SUPPLEMENTARY EXAM QUESTION PAPER JULY - 2017

    SUNSTAR PUBLICATION|Exercise PART-E|2 Videos

Similar Questions

Explore conceptually related problems

|(1+a^(2)-b^(2), 2ab, -2b),(2a, 1 -a^(2)+b^(2),2a),(2b, -2a, 1-a^2-b^2)|=(1 + a^2 + b^2)^(3) .

Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx and hence evaluate int_((pi)/(6))^((pi)/(3))(1)/(1+sqrt(tanx))dx.

Knowledge Check

  • int_0^(pi//2)(dx)/(1 + tanx) =

    A
    `pi`
    B
    `pi/2`
    C
    `pi/4`
    D
    `pi/3`

    • Similar Questions

    Explore conceptually related problems

    Prove that int_(a)^(b)(x)dx = int_(a)^(b)f(a+b-x)dx and int_(pi/4)^(pi/3)(dx)/(1+sqrt(tanx)) .

    Prove that int_(a)^(b) f(x)dx= int_(a)^(b) f (a+b-x)dx" hence evaluate " int_(0)^(pi/4) log(1+tan 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)^(b) f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx

    Prove that: int_a^b(f(x))/(f(x)+f(a+b-x))dx=(b-a)/2

    Prove that: |{:(a^(2)+1, ab, ac),(ab, b^(2)+1, bc):}|

    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

    Home
    Profile