Class 12 Mathematics - Chapter Integrals NCERT Solutions | Integrals sin 2x
Integrals sin 2x
The anti derivative of sin 2x is a function of x whose derivative is sin 2x.
It is known that,
\begin{align} \frac {d}{dx} (cos 2x) = 2 sin2x \end{align}
⇒ \begin{align} sin 2x =-\frac {1}{2} \frac {d}{dx}(cos 2x) \end{align}
∴ \begin{align} sin 2x = \frac {d}{dx}\left(-\frac {1}{2}cos 2x\right) \end{align}
Therefore, the anti derivative of sin2x is
\begin{align} sin 2x \;is -\frac {1}{2}cos 2x \end{align}
More Questions From Class 12 Mathematics - Chapter Integrals
- Q:- Integrals (ax + b)2
- Q:- sin 2x – 4e3x
- 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}
- 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:-
y = ex +1 : yn -y' = 0
- Q:-
Let f : N → N be defined by
State whether the function f is bijective. Justify your answer. - Q:- If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
- Q:-
Consider f : {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f –1 and show that (f –1)–1 = f.
- Q:-
Check the injectivity and surjectivity of the following functions:
(i) f : N → N given by f(x) = x2
(ii) f : Z → Z given by f(x) = x2
(iii) f : R → R given by f(x) = x2
(iv) f : N → N given by f(x) = x3
(v) f : Z → Z given by f(x) = x3
- 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:-
Answer the following as true or false.
\begin{align}(i) \overrightarrow{a}\; and\; \overrightarrow{-a}\; are\; collinear.\end{align}
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.
- Q:-
If f: R → R be given by f(x) =
, then fof(x) is
(A)
(B) x3
(C) x
(D) (3 – x3).
- 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:- Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.
- All Chapters Of Class 12 Mathematics
- All Subjects Of Class 12