Most Important Selected Qs for JEE AdvancedMathematicsArea Under Curves
Let P(x) be a polynomial satisfying _ x x^2 P(x) x^5+5 x+6 =2 and P(1)=2, P(2)=16 , P(3)=54 , then:
Options
- AP(4)=64
- BP(4)=128
- Carea bounded by y=f(x), x=0, x=2 and x -axis is 4 sq. units.
- Darea bounded by y=f(x), x=0, x=2 and x -axis is 8 sq. units.
Correct answer
D. area bounded by y=f(x), x=0, x=2 and x -axis is 8 sq. units.
Step-by-step solution
Clearly, P(x) is a polynomial of degree three with leading coefficient 2 . Clearly, P(x)=2 x^3 P(4)=128 and area = ₀^2 2 x^3 d x= ( x^4 2 )₀^2=8