Region R is enclosed by the curves and

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Region R is enclosed by the curves x=y2x = y^2 and x=y+2x = y + 2. Which of the following definite integrals correctly represents the area of R as a single integral? (a) ∫−12[y2−(y+2)] dy\displaystyle\int_{-1}^{2} \bigl[y^{2} - (y+2)\bigr] \, dy (b) ∫−12[(y+2)−y2] dy\displaystyle\int_{-1}^{2} \bigl[(y+2) - y^{2}\bigr] \, dy (c) ∫14[x−(x−2)] dx\displaystyle\int_{1}^{4} \bigl[\sqrt{x} - (x-2)\bigr] \, dx (d) ∫−12[(y+2)+y2] dy\displaystyle\int_{-1}^{2} \bigl[(y+2) + y^{2}\bigr] \, dy

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