Class 12 Mathematics - Chapter Integrals NCERT Solutions | \begin{align} \int \left(\frac {2-3sin x
\begin{align} \int \left(\frac {2-3sin x}{cos^2 x}\right) . dx\end{align}
\begin{align} \int \left(\frac {2-3sin x}{cos^2 x}\right) . dx\end{align}
\begin{align} =\int \left(\frac {2}{cos^2 x} - \frac{3sinx}{cos^2x}\right) . dx\end{align}
\begin{align} =2\int sec^2 x .dx - 3 \int tan x . sec x. dx\end{align}
\begin{align} =2 tan x - 3 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({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}
- Q:- \begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{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:- Evaluate the determinants
(i) \(\begin{vmatrix}3 & -1 & -2\\0 & 1 & 2\\0 & 0 & 4\end{vmatrix}\) (iii) \(\begin{vmatrix}3 & -4 & 5\\1 & 1 & -2\\2 & 3 & 1\end{vmatrix}\)
(ii) \(\begin{vmatrix}0 & 1 & 2\\-1 & 0 & -3\\-2 & 3 & 0\end{vmatrix}\)(iv) \(\begin{vmatrix}2 & -1 & -2\\0 & 2 & -1\\3 & -5 & 0\end{vmatrix}\) - Q:- Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
- Q:-
The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
- Q:-
The vertices of ΔABC are A (3, 5, −4), B (−1, 1, 2), and C (−5, −5, −2).
- Q:-
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
- Q:- If A=\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\), then show that |2A| = 4|A|
- Q:-
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
- Q:- Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b2} is neither reflexive nor symmetric nor transitive.
- Q:-
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}
- Q:- Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
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