Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2015MathematicsDefinite IntegrationActual

The value of _a^b x^7+ x x d x where a+b=0 is

Options

  1. A2 ~b - a ( b - a )
  2. Ba+3 b (b-a)
  3. Ca -( b - a ) b
  4. D0

Correct answer

D. 0

Step-by-step solution

aligned & a+b=0 a=-b & I= _ -b ^b x^7+ x x aligned Using property aligned & _ -a ^a f(x) d x= cases ₀^ 2 a f(x) d x & ; if f(x) is even 0 & ; if f(x) is odd cases & f(x)= x^7+ x x & f(-x)= (-x)^7+ (-x) (-x) = -x^7- x x & =- [ x^7+ x x ] aligned =- f ( x ) So f(x) is odd hence I =0

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(x) g(x) ,dx equal to ? 2026Passage: Let ₀^ 2 a x+b x (a+b)( x+ x) ,dx=k . Question: What is the value of k ? 2026Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(4-x) g(4-x) ,dx equal to ? 2026Passage: Let ₀^ 2 a x+b x (a+b)( x+ x) ,dx=k . Question: What is ₀^ 2 a x+b x x+ x ,dx equal to ? 2026Consider the following for the two (02) items that follow: Let f(x) = [x^2] , where [ ] is the greatest integer function. What is _ 2 ² f(x) , dx equal to? 2025What is _n^ n+1 (x - [x]) , dx , where [ ] is the greatest integer function and n is a natural number? 2025If I₁ = _e^ e^2 dx x and I₂ = ₁^2 e^x x , dx , then which one of the following is correct? 2025Paragraph: Let I = ₀^ 2 f(x) g(x) d x , where f(x)= x and g(x)= x+ x+1 . Question: What is ₀^ 2 d x g(x) equal to? 2024 Full Definite Integration list All NDA PYQs