If [x] is the greatest integer function,then | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $I = \int_0^5 [x] \, dx$. Since $[x]$ is the greatest integer function,it changes its value at every integer point. We can split the integral

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) Let $I = \int_0^5 [x] \, dx$. Since $[x]$ is the greatest integer function,it changes its value at every integer point. We can split the integral as: $I = \int_0^1 [x] \, dx + \int_1^2 [x] \, dx + \int_2^3 [x] \, dx + \int_3^4 [x] \, dx + \int_4^5 [x] \, dx$ $I = \int_0^1 0 \, dx + \int_1^2 1 \, dx + \int_2^3 2 \, dx + \int_3^4 3 \, dx + \int_4^5 4 \, dx$ $I = 0(1-0) + 1(2-1) + 2(3-2) + 3(4-3) + 4(5-4)$ $I = 0 + 1 + 2 + 3 + 4 = 10$.

If $[x]$ is the greatest integer function,then $\int_0^5 [x] \, dx =$

Similar Questions

$\int_1^4 \left(x + \sqrt{x} + \frac{1}{x}\right) dx - \int_1^{2 \log 2} dx = $

Suppose that $F(x)$ is an antiderivative of $f(x) = \frac{\sin x}{x}$,$x > 0$. Then $\int_{1}^{3} \frac{\sin 2x}{x} dx$ can be expressed as:

Evaluate the definite integral $\int_{-2}^{2.24} [x] \, dx$,where $[x]$ denotes the greatest integer function.

Evaluate the definite integral: $\int_0^1 \frac{dx}{\sqrt{1+x} - \sqrt{x}}$

The value $9 \int_0^9 \left[ \sqrt{\frac{10x}{x+1}} \right] dx$,where $[t]$ denotes the greatest integer less than or equal to $t$,is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module