Hi here is the question. Please solve a and b in the picture and show all your w

Question

Hi here is the question. Please solve a and b in the picture and show all your work to recieve full credit.

Let f(x) be an unknown function defined on [0,infinity_ with f(0) =0 and f(x) < x^2 for all x. For teach t >/= 0, let A_t be the area of the bounded region by y=x^2, y=2x^2, and y=t^2. Let B_t be the area of the region bounded by y=x^2, y=f(x), and x=t. See the picture below.

Let f(x) be an unknown function defined on [, infinity) with f() = and f(x) x2 for all x . For each t , let At be the area of the region bounded by y=x2 , y=2x2 and y=t2 . Let Bt be the area of the region bounded by y=x2 , y=f(x), and x=t. See the picture below. Show that if At=Bt for some t, then (Include your answer in Show My Work) Suppose At= Bt for all t Find f(x)

Explanation / Answer

(a) Follows from basic calculas that area b/w 2 curves is the integration of difference b/w them with proper limits.

integration(sqrt(y)-sqrt(y/2)) is area b/w y=x2 and x2/2.similarly for Right hand side part

(b) in left side substitute x=sqrt(y)

integration will become

(x-x/sqrt(2))*d(y)

=(x-x/sqrt(2))*d(x)*2x

equating both sides we get 2x^2-x^2*sqrt(2)=x^2-f(x)

solve for f(x)

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.