Definite Integrals of Odd, Even and Periodic Functions

JEE Main Mathematics · Definite Integration · 8 questions, latest first

• The value of the integral ∫_-1^1((x^3+|x|+1)/(x^2+2|x|+1)) d x is equal to:20266 April, Shift 2 · Q20
• The value of ∫_0^20 π( sin^4 x+ cos^4 x) d x is equal to:20262 April, Shift 2 · Q17
• The value of Σ_r=1^20(|√(π(∫_0^r x| sin π x| d x))|) is ____202628 January, Shift 1 · Q24
• Let [·] be the greatest integer function. If α=∫_0^64(x^1 / 3-[x^1 / 3]) d x, then 1/(π) ∫_0^α π((sin^2 θ)/(sin^6 θ+ cos^6 θ)) d…202622 January, Shift 2 · Q25
• The value of ∫_-π / 6^π / 6((π+4 x^11)/(1- sin (|x|+π / 6))) d x is equal to:202621 January, Shift 1 · Q17
• The value of the integral ∫_-1^2 log_e(x+√(x^2+1)) d x is20249 April, Shift 2 · Q12
• Let f(x)=∫_0^x g(t) log_e((1-t)/(1+t)) dt, where g is a continuous odd function. If ∫_-π / 2^π / 2(f(x)+(x^2 cos x)/(1+e^x)) d…202427 January, Shift 2 · Q25
• The value of the integral ∫_-(π)/4^((π)/4) (x+(π)/4)/(2- cos 2 x) d x is:20231 February, Shift 2 · Q70