Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201921 Apr 2019Evening ShiftMathematicsArea Under CurvesActual

The area (in sq. units) bounded by the curve y = x 2 + 2 x + 1 and the tangent to it at ( 1 , 4 ) and the Y -axis is

Options

  1. A1 3 sq. units
  2. B2 3 sq. units
  3. C1 sq. units
  4. D7 3 sq. units

Correct answer

A. 1 3 sq. units

Step-by-step solution

The equation is given as, y = x 2 + 2 x + 1 Differentiate the above equation with respect to x , d y d x = 2 x + 2 At ( 1 , 4 ) d y d x = 2 1 + 2 = 4 The figure below represents the area bounded. The bounded area is, A = ∫ 0 1 y d x - 1 2 ( O A × A P ) ⇒ A = ∫ 0 1 x 2 + 2 x + 1 d x - 1 2 1 × 4 ⇒ A = x 3 3 + x 2 + x 0 1 - 2 ⇒ A = 1 3 + 1 2 + 1 - 0 - 2 ⇒ A = 1 3 sq. units

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5 2026The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026 Full Area Under Curves list All AP EAMCET PYQs