Class 12 Mathematics - Chapter Integrals NCERT Solutions | \begin{align} \int \frac{x^3 + 3x + 4}{\
\begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align}
\begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align}
\begin{align} =\int \left(x^\frac{5}{2} + 3x^\frac{1}{2} + 4x^\frac{1}{2}\right) . dx\end{align}
\begin{align} =\frac{\left(x^{\displaystyle\frac72}\right)}{\displaystyle\frac72}+ \frac{3\left(x^{\displaystyle\frac32}\right)}{\displaystyle\frac32} + \frac{4\left(x^{\displaystyle\frac12}\right)}{\displaystyle\frac12} + C\end{align}
\begin{align} =\frac27\left(x^\frac72\right)+ 2\left(x^\frac32\right) + 8\left(x^\frac12\right) + C\end{align}
\begin{align} =\frac27\left(x^\frac72\right)+ 2\left(x^\frac32\right) + 8\left(\sqrt x\right) + C\end{align}
More Questions From Class 12 Mathematics - Chapter Integrals
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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:- Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{\sqrt2}\right)\end{align}
- Q:- Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = { (a,b) ; |a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
- 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:-
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
- Q:-
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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- Q:-
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}
- 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:-
Determine order and degree(if defined) of differential equation (ym)2 + (yn)3 + (y')4 + y5 =0
- Q:-
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
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