Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Using integration, find the area of the triangle ABC, coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4)

Using integration, find the area of the triangle ABC, coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4)

Grade:

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
i)Area of an enclosed region bounder by the curve y = f(x), x-axis and the boundaries,x = a to b is given by A = ∫f(x) dx in [x = a to b]
ii) Hence, here the area of the triangle ABC is enclosed by the lines AB, BC & CA; its area by integration is given by Area under AB + Area under BC - Area under AC
iii) Using two point form equation of AB, Bc & CA are respectively:
y = (5x - 18)/2; y = (12 - x) and y = (3x - 8)/4
iv) Area under AB = ∫(5x - 18)/2 dx in [4 to 6] = (1/2[5x²/2 - 18x] in [4 to 6]
Evaluating for the limits, A1 = (1/2)[(90 - 108) - (40 - 72)] = 7
Similarly area under BC = (12x - x²/2) in [6 to 8] = 10
Area under AC = (1/4)(3x²/2 - 8x) in [4 to 8] = 10
Hence net area = 7 + 10 - 10 = 7 sq units.
Thanks and Regards
Shaik Aasif
askIITians faculty
ankit singh
askIITians Faculty 614 Points
9 months ago

The equations of sides of the triangles are y=2x+1,y=3x+1, and x=4.
On solving these question, we obtain the vertices of triangle as A(0,1),B(4,13), and C(4,9).
It can be observed that,
Area(ΔACB)=Area(OLBAO)Area(OLCAO)
=04(3x+1)dx04(2x+1)dx
=[23x2+x]04[22x2+x]04
=(24+4)(16+4)
=2820=8sq. units.

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free