Definite Integration – JEE Main Practice Test

The value of the integral ∫₀^{π/4} x dx / (sin⁴(2x) + cos⁴(2x)) is:

If the shortest distance between the lines (x+2)/2 = (y+3)/3 = (z−5)/4 and (x−3)/1 = (y−2)/(−3) = (z+4)/2 is (38 / 3√5) k and ∫₀ᵏ [x²] dx = α − √α, then 6α³ equals:

If β(m,n)=∫₀¹ x^{m−1}(1−x)^{n−1} dx and ∫₀¹ (1−x¹⁰)²⁰ dx = a·β(b,c), then 100(a+b+c) equals:

If limₜ→0 ( ∫₀¹ (3x+5)ᵗ dx )^{1/t} = (α/5e)(8/5)^{2/3}, then α equals:

Let [.] denote greatest integer function. If ∫₀^{e³} [1 / e^{x−1}] dx = α − ln 2, then α³ equals:

The value of the integral ∫₀^π 8x dx / (4cos²x + sin²x) is:

Let f(x)+f(π−x)=π² for all x. Then ∫₀^π f(x) sin x dx equals:

The value of 9∫₀⁹ [ √(10x/(x+1)) ] dx is:

If ∫_{π/6}^{π/3} √(1−sin2x) dx = α + β√2 + γ√3, then (3α + 4β − γ) equals:

Let f(x)=∫_{−x}^{x} (|t|−t²)e^{−t²}dt and g(x)=∫₀^{x²} t^{1/2}e^{−t}dt. Value of 9[f(√ln9)+g(√ln9)] equals: