Mathematics

Using definite integration, find area of the triangle with vertices at A(1,1),B(3,3)A(1,1),B(3,3).


SOLUTION
$$e{q^n}\,of\,AB:$$
$$y - 1 = \frac{2}{2}\left( {x - 1} \right)$$
$$y - 1 = x - 1$$
$$y = x$$
$$e{q^n}\,of\,BC:$$
$$y - 3 = \frac{{ - 2}}{1}\left( {x - 3} \right)$$
$$y - 3 =  - 2x + 6$$
$$2x + y = 9$$
$$Area = \int_1^3 {xdx}  + \int_3^4 {\left( {9 - 2x} \right)dx} -\int\limits_1^4 1 dx$$
$$ = \left( {\frac{{{x^2}}}{2}} \right)_1^3 + \left( {9x - {x^2}} \right)_3^4-3$$
$$ = \frac{9}{2} - \frac{1}{2} + \left[ {\left( {36 - 16} \right) - \left( {27 - 9} \right)} \right]-3$$
$$ = \dfrac{8}{2} + \left( {20 - 18} \right)-3$$
$$ = 4+ 2-3$$
$$=3$$.
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Solve:
$$\displaystyle \int_{2}^{3} \cfrac{x d x}{x^{2}+1}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Find the integral of    $$\displaystyle \int (ax^2+bx+c)dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Assertion & Reason Hard
ASSERTION

The value of $$\displaystyle \int_{0}^{\pi }xf\left ( \sin x \right )dx$$ is $$\displaystyle \frac{\pi }{2}\displaystyle \int_{0}^{\pi }f\left ( \sin x \right )dx$$ or $$\pi \displaystyle \int_{0}^{\pi /2}f\left ( \sin x \right )dx$$

REASON

$$\displaystyle \int_{0}^{a}f\left ( x \right )dx=\displaystyle \int_{0}^{a}f\left ( a-x \right )dx$$ and $$\displaystyle \int_{0}^{2a}f\left ( x \right )dx=2\displaystyle \int_{0}^{a}f\left ( x \right )dx$$ If $$f\left ( 2a-x \right )=f\left ( x \right )$$

  • A. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • B. Assertion is correct but Reason is incorrect
  • C. Both Assertion and Reason are incorrect
  • D. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
$$\int {\sqrt {\dfrac{{1 - x}}{{1 + x}}} } \,dx =$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Hard
Evaluate:
$$\displaystyle \int { \cfrac { dx }{ x(x+2) }  } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer