definite integral

If the value of the double integral $\int_{x=3}^{4} \int_{y=1}^{2} \frac{dydx}{(x + y)^2}$ is $\log_e(\frac{a}{24})$, then $a$ is __________ (answer in integer).

Consider the definite integral $\int^2_1(4x^2+2x+6)dx$ Let I e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals...

Given $\int^{\infty}_{-\infty}e^{-x^2}dx=\sqrt{\pi}$ If a and b are positive integers, the value of $\int^{\infty}_{-\infty}e^{-a(x+b)^2}dx$ is _________.

Define [x] as the greatest integer less than or equal to x, for each x ϵ (-∞, ∞). If y = [x], then area under y for x ϵ [1,4] is

The value of the following definite integral is _________ (round off to three decimal places) $\int_{1}^{e} (x \ln x) dx$

Simpson's $${1 \over 3}$$ rule is used to integrate the function $$f\left( x \right) = {3 \over 5}{x^2} + {9 \over 5}\,\,$$ between $$x=0$$ and $$x=1$$ using the least number of eq...

The definite integral $$\,\int\limits_1^3 {{1 \over x}} dx\,\,$$ is evaluated using Trapezoidal rule with a step size of $$1.$$ The correct answer is

The value of the integral $$\int\limits_0^2 {{{{{\left( {x - 1} \right)}^2}\sin \left( {x - 1} \right)} \over {{{\left( {x - 1} \right)}^2} + \cos \left( {x - 1} \right)}}dx} $$ is

Using the trapezoidal rule, and dividing the interval of integration into three equal sub-intervals, the definite integral $$\,\,\int\limits_{ - 1}^{ + 1} {\left| x \right|dx\,\,}...

The value of the definite integral $$\int_1^e {\sqrt x \ln \left( x \right)dx} $$ is

The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is

The integral $$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,} $$ when evaluated by using simpson's $$1/{3^{rd}}$$ rule on two equal sub intervals each of length $$1,$$ equals to

If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $$ equals ________.

The parabolic are $$y = \sqrt x ,1 \le x \le 2$$ is revolved around the $$x$$-axis. The volume of the solid of revolution is

The value of the integral $$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$

The area enclosed between the curves $${y^2} = 4x\,\,$$ and $${{x^2} = 4y}$$ is

The length of the curve $$\,y = {2 \over 3}{x^{3/2}}$$ between $$x=0$$ & $$x=1$$ is

$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$ is equal to

Area bounded by the curve $$y = {x^2}$$ and the lines $$x=4$$ and $$y=0$$ is given by

The area bounded by the parabola $$2y = {x^2}$$ and the lines $$x=y-4$$ is equal to _________.

The value of $$\int\limits_0^\infty {{e^{ - {y^3}}}.{y^{1/2}}} $$ dy is _________.