Class 12 Mathematics - Chapter Integrals NCERT Solutions | \begin{align} \int \frac{x^3 + 5x^2 - 4}
\begin{align} \int \frac{x^3 + 5x^2 - 4}{x^2} . dx\end{align}
\begin{align} \int \frac{x^3 + 5x^2 - 4}{x^2} . dx\end{align}
\begin{align} =\int \left(x + 5 - 4x^{-2}\right) . dx\end{align}
\begin{align} =\int x .dx + 5 \int 1.dx- 4 \int x^{-2} .dx\end{align}
\begin{align} =\frac {x^2}{2} + 5x + 4 \left(\frac{x^{-1}}{-1}\right) + C\end{align}
\begin{align} =\frac {x^2}{2} + 5x + \frac{4}{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:- 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\left(1-x\right).\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:-
Determine order and degree(if defined) of differential y' + y =ex
- Q:-
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
- Q:- If A=\(\begin{bmatrix}1 & 0 & 1\\0 & 1 & 2\\0 & 0 & 4\end{bmatrix}\), then show that |3A| = 27|A|.
- Q:- Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related?
- Q:-
Represent graphically a displacement of 40 km, 30° east of north.
- Q:- Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{2}\right)\end{align}
- 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:- Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.
- Q:- Find the principal value of \begin{align} sec^{-1}\left(\frac{2}{\sqrt3}\right)\end{align}
- Q:- Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{\sqrt2}\right)\end{align}
- All Chapters Of Class 12 Mathematics
- All Subjects Of Class 12