\begin{align} \int \left({a}{x^2} + bx + c\right) .dx\end{align}
\begin{align} =a\int {x^2}.dx + b\int x.dx + c\int 1.dx \end{align}
\begin{align} =a\left(\frac {x^3}{3}\right) + b\left(\frac {x^2}{2}\right) + cx + C\end{align}
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
Represent graphically a displacement of 40 km, 30° east of north.
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
y = Ax : xy' = y (x ≠ 0)
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
Determine order and degree(if defined) of differential equation \begin{align}\frac{d^2y}{dx^2}=\cos3x + sin3x\end{align}
The total revenue in Rupees received from the sale of x units of a product is given by
R (x) = 13x2 + 26x + 15
Find the marginal revenue when x = 7.
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?