∫(1-x)-2 dx = (1-x)-1+c - Mathematics and Statistics

Question

$\int {(1 - x)}^{- 2}$ dx = ${(1 - x)}^{- 1} + c$

Options

True
False

MCQ

True or False

Solution

This statement is True.

Explanation:

$\int {(1 - x)}^{- 2} . d x$

= $\frac{{(1 - x)}^{- 2 + 1}}{(- 2 + 1) \times (- 1)} + c$

= $\frac{{(1 - x)}^{- 1}}{(- 1) (- 1)} + c$

= ${(1 - x)}^{- 1} + c$

shaalaa.com

Methods of Integration: Integration by Substitution

Is there an error in this question or solution?

Q 1.B.ii Q 1.B.i Q 1.B.iii

2022-2023 (March) Official

APPEARS IN

2022-2023 (March) Official (with solutions)

Q 1.B.ii | 1 mark

RELATED QUESTIONS

Evaluate :

$\int \frac{1}{\sin^{4} x + \sin^{2} x \cos^{2} x + \cos^{4} x} d x$

Integrate the functions:

$\frac{{(1 + \log x)}^{2}}{x}$

Evaluate: $\int_{0}^{3} f (x) d x$ where f(x) = ${\begin{cases} \cos 2 x & 0 \leq x \leq \frac{π}{2} \\ 3 & \frac{π}{2} \leq x \leq 3 \end{cases}$

Write a value of $\int tan x \sec^{3} x d x$

Evaluate the following integrals : $\int \frac{\sin 2 x}{\cos x} d x$

Evaluate the following integrals : $\int \cos^{2} x . d x$

Integrate the following functions w.r.t. x : $\frac{{(\sin^{- 1} x)}^{\frac{3}{2}}}{\sqrt{1 - x^{2}}}$

Integrate the following functions w.r.t. x : $\frac{e^{3 x}}{e^{3 x} + 1}$

Integrate the following functions w.r.t. x : sin⁴x.cos³x

Integrate the following functions w.r.t. x : $\frac{\cos 3 x - \cos 4 x}{\sin 3 x + \sin 4 x}$

Evaluate the following : $\int \frac{1}{\sqrt{2 x^{2} - 5}} . d x$

Evaluate the following : $\int \sqrt{\frac{9 + x}{9 - x}} . d x$

Evaluate the following : $\int \frac{1}{1 + x - x^{2}} . d x$

Evaluate the following : $\frac{1}{4 x^{2} - 20 x + 17}$

Evaluate the following : $\int \frac{1}{4 + 3 \cos^{2} x} . d x$

Integrate the following functions w.r.t. x : $\int \frac{1}{2 \sin 2 x - 3} d x$

Integrate the following functions w.r.t. x : $\int \frac{1}{3 + 2 \sin 2 x + 4 \cos 2 x} . d x$

Integrate the following functions w.r.t. x : $\int \frac{1}{\cos x - \sin x} . d x$

Evaluate the following integrals : $\int \sqrt{\frac{e^{3 x} - e^{2 x}}{e^{x} + 1}} . d x$

Evaluate $\int \frac{3 x^{3} - 2 \sqrt{x}}{x}$ dx

Fill in the Blank.

$\int \frac{5 (x^{6} + 1)}{x^{2} + 1}$ dx = x⁴ + ______ x³ + 5x + c

If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.

$\int \frac{d x}{1 + e^{- x}}$ = ______

The general solution of the differential equation $(1 + \frac{y}{x}) + \frac{d y}{d x}$ = 0 is ______.

$\int {(7 x - 2)}^{2} d x = \frac{{(7 x - 2)}^{3}}{21} + c$

$\int \frac{x + \sin x}{1 + \cos x} d x$ is equal to ______.

Write $\int \cot x d x$ .

Evaluate the following.

$\int \frac{1}{x^{2} + 4 x - 5} d x$

Evaluate the following.

$\int x \sqrt{1 + x^{2}} d x$

Evaluate $\int (1 + x + \frac{x^{2}}{2!}) d x$

∫(1-x)-2 dx = (1-x)-1+c - Mathematics and Statistics

Advertisements

Advertisements

Question

Options

Solution

APPEARS IN

RELATED QUESTIONS

Select a course

∫(1-x)-2 dx = (1-x)-1+c - Mathematics and Statistics

Advertisements

Advertisements

Question

Options

SolutionShow Solution

APPEARS IN

RELATED QUESTIONS

Select a course

Solution