Question Solved1 Answer 1. Define A(x) to be the area bounded by the t (horizontal) and y axes, the line y=t+1, and the vertical line at x (Fig. 14). For example, A(4) = 12. a) Evaluate A(0), A(1), A(2), A(2.5) and A(3). b) What area would A(3) - A(1) represent in the figure? c) Graph y= A(x) for 0 < x < 4. AXY y=1t < A(x) = area X Fig. 14
TWQOM9 The Asker · Calculus
Transcribed Image Text: 1. Define A(x) to be the area bounded by the t (horizontal) and y axes, the line y=t+1, and the vertical line at x (Fig. 14). For example, A(4) = 12. a) Evaluate A(0), A(1), A(2), A(2.5) and A(3). b) What area would A(3) - A(1) represent in the figure? c) Graph y= A(x) for 0 < x < 4. AXY y=1t < A(x) = area X Fig. 14
More Transcribed Image Text: 1. Define A(x) to be the area bounded by the t (horizontal) and y axes, the line y=t+1, and the vertical line at x (Fig. 14). For example, A(4) = 12. a) Evaluate A(0), A(1), A(2), A(2.5) and A(3). b) What area would A(3) - A(1) represent in the figure? c) Graph y= A(x) for 0 < x < 4. AXY y=1t < A(x) = area X Fig. 14
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on solving i found that A(x) is a parabola and the coefficientof x2 is positive so it will open upwardand its local minimum exist for that value x where itsderivative is equal to = 01 Solution{:[area=A(x)=int_(0)^(x)(1+t)dt],[A(x)=[t+(t^(2))/(2)]_(0)^(x)],[A(x)=x+(x^(2))/(2)]:}(a){:[:.A(0)=0+0=0],[A(1)=1+(1)/(2)=(3)/(2)=1.5],[A(2)=2+(2^(2))/(2)=4 ... See the full answer