Home · NDA PYQs · Mathematics · Definite Integration

NDA Definite Integration PYQs with Solutions

110 previous year questions from Definite Integration (NDA Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

110 questionsMathematics2010–2026Answers + solutions

About Definite Integration PYQs

Definite Integration has 110 previous year questions in the Quantrex Academy NDA Mathematics bank. The 110 questions in this list come from NDA (110), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Definite Integration PYQs with Solutions

About Definite Integration PYQs

Questions by year (this list)

Definite Integration questions with solutions

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 ?

Passage: Let ∫_0^ (π)/(2) (a x+b x)/((a+b)( x+ x))\,dx=k . Question: What is the value of k ?

Passage: 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 ?

Passage: Let ∫_0^ (π)/(2) (a x+b x)/((a+b)( x+ x))\,dx=k . Question: What is ∫_0^ (π)/(2) (a x+b x)/( x+ x)\,dx equal to ?

Consider 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?

What is ∫_n^ n+1 (x - [x])\, dx , where [·] is the greatest integer function and n is a natural number?

If I_1 = ∫_e^ e^2 (dx)/( x) and I_2 = ∫_1^2 (e^x)/(x)\, dx , then which one of the following is correct?

Paragraph: Let I=∫_0^ (π)/(2) (f(x))/(g(x)) d x , where f(x)= x and g(x)= x+ x+1 . Question: What is ∫_0^ (π)/(2) (d x)/(g(x)) equal to?

Paragraph: Let f(t)= (t+ 1+t^2 ) and g(t)= (f(t)) . Question: What is ∫_ -π ^π g(t) d t equal to?

Paragraph: Let f(x)=|x^2-x-2| Question: What is ∫_0^2 f(x) d x equal to?

What is ∫_ -1 ^1(3 x- 3 x) ^2 x d x equal to?

What is ∫_0^ (π)/(2) (a+ x)/(2 a+ x+ x) d x equal to?

Let p=∫_a^b f(x) d x and q=∫_a^b|f(x)| d x . If f(x)=e^ -x , then which one of the following is correct?

Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What is ∫_0^2 h(x) d x equal to?

Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What is ∫_ -1 ^0 h(x) d x equal to?

Let 3 f(x)+f((1)/(x))=(1)/(x)+1 What is 8 ∫_1^2 f(x) d x equal to?

Let ϕ(a)=∫_a^ a+100 π | x| d x What is ϕ(a) equal to?

Let ϕ(a)=∫_a^ a+100 π | x| d x What is ϕ^ (a) equal to?

Paragraph: Let I=∫_0^ (π)/(2) (f(x))/(g(x)) d x , where f(x)= x and g(x)= x+ x+1 . Question: What is I equal to?

Paragraph: Let f(x)=|x^2-x-2| Question: What is ∫_1^3 f(x) d x equal to?

Let I=∫_ -2 π ^ 2 π ( ^4 x+ ^4 x)/(1+3^x) d x What is I equal to?

Let I=∫_ -2 π ^ 2 π ( ^4 x+ ^4 x)/(1+3^x) d x What is ∫_0^π( ^4 x+ ^4 x) d x equal to?

What is ∫_0^ 8 π | x| d x equal to?

Paragraph: Let l=∫_a^b (|x|)/(x) d x, a Question: What is l equal to when a < 0 < b ?

Paragraph: Let l=∫_a^b (|x|)/(x) d x, a Question: What is l equal to when a < b < 0 ?

Paragraph: Let I_1=∫_0^π (x)/(1+ ^2 x) d x and I_2=∫_0^π (1)/(1+ ^2 x) d x Question: What is the value of I_2 ?

Paragraph: Let I_1=∫_0^π (x)/(1+ ^2 x) d x and I_2=∫_0^π (1)/(1+ ^2 x) d x Question: What is the value of (I_1+I_2)/(I_1-I_2) ?

Paragraph: Let I_1=∫_0^π (x)/(1+ ^2 x) d x and I_2=∫_0^π (1)/(1+ ^2 x) d x Question: What is the value of 8 I_1^2 ?

What is ∫_0^1 ((1)/(x)-1) d x equal to?

If ∫_0^ π / 2 ( ^4 x+ ^4 x) d x=k , then what is the value of ∫_0^ 20 π ( ^4+ ^4 x) d x ?

What is ∫_0^ (π)/(4) (d x)/(( x+ x)^2) equal to?

What is ∫_ -2 ^ -1 (x)/(|x|) d x equal to?

What is ∫_ -π / 2 ^ π / 2 (e^ x x+e^ x x) d x equal to?

If f(x)=2^x , then what is ∫_2^ 10 f^ (x) f(x) d x equal to?

What is ∫_0^ (π)/(2) e^ ( x) d x equal to?

What is ∫_0^π ( (x)/(2)) d x equal to?

What is ∫_0^a (f(a-x))/(f(x)+f(a-x)) d x equal to?

If ∫_0^a[f(x)+f(-x)] d x=∫_ -a ^a g(x) d x then what is g(x) equal to?

If f(x) satisfies f(l)=f(4) , then what is ∫_1^4 f^ (x) d x equal to?

If ∫_ -2 ^0 f(x) d x=k , then ∫_ -2 ^0|f(x)| d x is

What is the value of ∫_0^ π / 4 ( ^3 x+ x) d x ?

Paragraph: Consider the integrals I_1=∫_0^x (x d x)/(1+ x) and I_2=∫_0^π ((π-x) d x)/(1- (π+x)) Question: What is the value of I_1 ?

∫_0^ (π)/(2) | x- x| d x is equal to

∫_0^ (π)/(2) e^ x x d x is equal to

Paragraph: Consider the integrals I_1=∫_0^x (x d x)/(1+ x) and I_2=∫_0^π ((π-x) d x)/(1- (π+x)) Question: What is the value of I_1+I_2 ?

What is ∫_a^b[x] d x+∫_a^b[-x] d x equal to, where[.] is the greatest integer function?

What is ∫_2^8|x-5| d x equal to?

What is ∫_ -1 ^1\ (d)/(d x)( ^ -1 (1)/(x))\ d x equal to?

What is ∫_0^π ^ x x d x equal to?

What is ∫_1^ e x x dx equal to?

What is ∫_0^ 2 [x^2] d x equal to (where [.] is the greatest integer function)?

What is the value of ∫_ (-π)/(4) ^ (π)/(4) ( x - x) d x ?

If ∫_a^b x^3 d x=0 and ∫_a^b x^2 d x=(2)/(3) , then what are the values of a and b respectively?

What is ∫_0^1 x(1-x)^9 d x equal to?

What is ∫_0^ (π)/(2) (d θ)/(1+ θ) equal to?

What is ∫_0^ 2 π 1+ (x)/(2) d x equal to?

If f(x) and g(x) are continuous functions satisfying f(x)=f(a-x) and g(x)+g(a-x)=2 , then what is ∫_0^ a f(x) g(x) dx equal to?

The value of ∫_0^ (π)/(4) x d x+∫_0^ (π)/(4) x d x is equal to

What is ∫_ ^ -1 ^ e^2 | x x | dx equal to?

If ∫_0^ π / 2 dx 3 x+5 = ^ -1 ^ -1 2 , then what is the value of K ?

Let f(x) be a function such that f^ ((1)/(x))+x^3 f^ (x)=0 , What is ∫_ -1 ^1 f(x) d x equal to?

What is ∫_1^3|1-x^4| dx equal to?

Consider the functions f(x)=x g(x) and g(x)= [(1)/(x)] Where [ ·] is the greatest integer function. What is ∫_ (1)/(3) ^ (1)/(2) g(x) d x equal to?

Given that a_ n =∫_0^π ^2\ (n+1) x\ 2 x dx What is a_ n-1 -a_ n-4 equal to ?

Consider the functions f(x)=x g(x) and g(x)= [(1)/(x)] Where [·] is the greatest integer function. What is ∫_ (1)/(3) ^1 f(x) d x equal to ?

Given that a_ n =∫_0^π ^2\ (n+1) x\ 2 x dx Consider the following statements: 1. The sequence \ a_ 2 n \ is in AP with common difference zero. 2. The sequence \ a_ 2 n+1 \ is in

If ∫_ -2 ^5 f(x) d x=4 and ∫_0^5\ 1+f(x)\ d x=7 , then what is ∫_ -2 ^0 f(x) d x equal to?

What is ∫_0^ 4 π | x| dx equal to?

What is ∫_ -2 ^2 x d x-∫_ -2 ^2[x] d x equal to, where [·] is the greatest integer function?

The value of ∫_a^b (x^7+ x)/( x) d x where a+b=0 is

Consider the integrals A=∫_0^π ( x d x)/( x+ x) and B=∫_0^π ( x d x)/( x- x) Which one of the following is correct?

If 0 < a < b , then ∫_a^b (|x|)/(x) d x is equal to

Consider the integrals A=∫_0^π ( x d x)/( x+ x) and B=∫_0^π ( x d x)/( x- x) What is the value of B ?

Consider the integral I_m=∫_0^π ( 2 m x)/( x) d x , where m is a positive integer. . Consider the following: 1. I_m-I_ m-1 is equal to 0. 2. I_ 2 m > I_m Which of the above is/are

Consider the integral I_m=∫_0^π ( 2 m x)/( x) d x , where m is a positive integer. What is I_m equal to?

∫_ -1 ^1 x|x| dx is equal to