Find the area of the closed figure bounded by x = –1, y = 0, y = x 2 + x + 1 and the tangent to the curve y = x 2 + x + 1 at (1, 3).
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. We have,
y = x 2 + x + 1
⇒ 
= 2x + 1
⇒ 
= 3
The equation of the tangent to y= x 2 + x + 1 at (1, 3) is y –3 = 3(x –1) ⇒ y = 3x
The equation y = x 2 + x + 1 represents a parabola opening upward and having vertex at
. Its graph is shown in fig. The area enclosed by x = –1, y = 0, y = x 2 + x + 1 and y = 3x is shaded in fig. We slice the shaded region into vertical strips.
Required area = Area of region OABC + Area of region OCD
= 
+ 
= 
+ 
= 
+ 
= – 
+ 
= 
sq. units.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems