Class 12 Mathematics - Chapter Integrals NCERT Solutions | \begin{align} \int sec x . \left(sec x +
\begin{align} \int sec x . \left(sec x + tan x\right) .dx \end{align}
\begin{align} \int sec x . \left(sec x + tan x\right) .dx \end{align}
\begin{align} =\int \left(sec^2 x + sec x . tan x\right) .dx \end{align}
\begin{align} =\int sec^2 x . dx + \int sec x . tan x .dx \end{align}
\begin{align} = tan x + sec x + C \end{align}
More Questions From Class 12 Mathematics - Chapter Integrals
- Q:- Integrals (ax + b)2
- Q:- sin 2x – 4e3x
- Q:- Integrals sin 2x
- Q:- \begin{align} \int \left(\sqrt{x} - \frac {1}{\sqrt{x}}\right)^2 .dx\end{align}
- Q:- \begin{align} \int \frac{x^3 + 5x^2 - 4}{x^2} . dx\end{align}
- Q:- Integrals e2x
- Q:- \begin{align} \int \left(\frac {2-3sin x}{cos^2 x}\right) . dx\end{align}
- Q:- \begin{align} \int \left({2}{x^2} + e^x\right) .dx\end{align}
- Q:- Integrals cos3x
- Q:- \begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align}
Popular Questions of Class 12 Mathematics
- Q:-
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
- Q:-
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
- Q:-
Represent graphically a displacement of 40 km, 30° east of north.
- Q:-
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
- Q:-
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
- Q:-
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
- Q:- Evaluate the determinants
\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
- Q:-
A particle moves along the curve 6y = x3 + 2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.
- Q:- Find the principal value of \begin{align} cot^{-1}\left(\sqrt3\right)\end{align}
- Q:-
The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
- Q:- The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?
- Q:-
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.
- Q:-
A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
- Q:-
Consider f : R+ → [– 5, ∞) given by f(x) = 9x2 + 6x – 5. Show that f is invertible
with
. - Q:- If A = \(\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}\), Find |A|
- Q:-
Let f : R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
- Q:-
Determine order and degree(if defined) of differential equation
\begin{align}\left(\frac{d^2y}{dx^2}\right)^2\;+\;cos\left(\frac{dy}{dx}\right)\;=\;0\end{align}
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