Consider the region T that lies between the curve and the –axis for .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the region T that lies between the curve

x=e^{\tfrac{y}{2}}-1

and the

y

–axis for

0\le y\le 4

. (1) Write an integral expression for the area of region T and evaluate the integral exactly. (2) Use the exact value from part (a) to compute a decimal approximation of the area, rounded to the nearest thousandth. (3) Suppose a thin plate occupying region T has constant density

\delta

(mass per unit area). Write an expression for the mass of the plate in terms of

\delta

and determine its value when

\delta=0.40\,\text{kg}\,\text{m}^{-2}

. Include appropriate units in your answer.

Related theory

Applications of Integration
Area Applications
Area under a curve
Area under simple curves

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