Class 12 Mathematics - Chapter Integrals NCERT Solutions | \begin{align} \int \frac {sec^2 x}{Coses
\begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}
\begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}
\begin{align} =\int \left(\frac{\frac {1}{Cos^2 x}}{\frac{1}{sin^2 x}}\right) . dx\end{align}
\begin{align} =\int \left(\frac{Sin^2x}{Cos^2x}\right) . dx\end{align}
\begin{align} =\int tan^2 x . dx\end{align}
\begin{align} =\int \left(sec^2x - 1\right) . dx\end{align}
\begin{align} =\int sec^2x . dx - \int 1. dx\end{align}
\begin{align} = tanx - x + C\end{align}
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Popular Questions of Class 12 Mathematics
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Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
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Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
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Represent graphically a displacement of 40 km, 30° east of north.
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If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
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Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
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Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
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\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - Q:- Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y} - Q:- Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm - Q:-
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).
Recently Viewed Questions of Class 12 Mathematics
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Find the direction cosines of a line which makes equal angles with the coordinate axes.
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Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.
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The radius of an air bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?
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Let f, g and h be functions from R to R. Show that
(f + g)oh = foh + goh
(f . g)oh = (foh) . (goh)
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Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
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(a) r = 3 cm
(b) r = 4 cm - Q:-
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
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