Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202418 May 2024Morning ShiftMathematicsArea Under CurvesActual

The area of the region (in sq. units) enclosed by the curve y=x^3-19 x+30 and the x -axis is

Options

  1. A167 2
  2. B517 2
  3. C36
  4. D72

Correct answer

B. 517 2

Step-by-step solution

Given the curve, y=x^3-19 x+30 y=(x+5)(x-2)(x-3) = _ -5 ^2 y d x- ₂^3 y d x= _ -5 ^2 (x^3-19 x+30 ) d x- ₂^3 (x^3-19 x+30 ) d x= ( x^4 4 - 19 x^2 2 +30 x )_ -5 ^2- ( x^4 4 - 19 x^2 2 +30 x )₂^3=(4-38+60)- ( 625 4 - 475 2 -150 ) aligned & - ( 81 4 - 171 2 +90 )+(4-38+60)= 1029 4 + 5 4 & = 517 2 sq. units aligned

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