Mathematics · 2016
JEE Main · 10 April 2016, Shift 1 · Q75
The value of the integral ∫_4^10 ([x^2] d x)/([x^2-28 x+196]+[x^2]), where [x] denotes the greatest integer less than or equal to x, is:
The value of the integral
$$\int_4^{10} \frac{\left[x^2\right] d x}{\left[x^2-28 x+196\right]+\left[x^2\right]} \text {, where }[x]
$$
denotes the greatest integer less than or equal to $\displaystyle x$, is :
Official answer
(2)
$\displaystyle 3$
More from Definite Integration
- Let function F be defined as F(x)=∫_1^x (e^t)/t dt, x>0 then the value of the integral ∫_1^x (e^t)/(t+a) dt, where a>0, is:2014
- If the value of the integral ∫_0^5 (x+[x])/(e^x-[x]) d x=α e^-1+β, where α, β ∈ R, 5 α+6 β=0, and [x] denotes the greatest integer less than or equal…2021
- If for all real triplets (a, b, c), f(x)=a+b x+cx^2; then ∫_0^1 f(x) d x is equal to:2020
- The integral ∫_0^(1/2) (ln (1+2 x))/(1+4 x^2) d x, equals:2014
- If the value of the integral ∫_0^1 / 2 x^2/((1-x^2)^3 / 2) d x is k/6, then k is equal to:2020
- Let 0 ≤ x ≤ 2Max{(9-x^2)/(5-x)}=α and 0 ≤ x ≤ 2Min{(9-x^2)/(5-x)}=β. If ∫_β-8/3^2 α-1 Max{(9-x^2)/(5-x), x} d x=α_1+α_2 log_e(8/15) then α_1+α_2 is…2022
- Let the function f:[0,2] → R be defined as f(x)= {e^min {x^2, x-[x]}, x ∈[0,1); e^[x- log_e x], x ∈[1,2]} where [t] denotes the greatest integer less…2023
- If ∫_1^2 (d x)/((x^2-2 x+4)^(3/2))=k/(k+5), then k is equal to:2017
JEE Main 2016 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.