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
- A167 2
- B517 2
- C36
- 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