08.03 Finding the Area Between Curves

Let R be the area of the region between x = ey − 3 and x equals the square root of y for 0.5 < x < 1.5. What is R?

R equals the integral from one fourth to 2 and one fourth of square root of y minus e to the power of quantity y minus 3 close quantity dy

Select the valid statement(s) for the area bounded between y = 3sinx and y equals 2 times the square root of x comma where 3 sine x equals 2 times the square root of x at (0, 0) and (0.48, 1.386). I:the integral from 0 to 48 hundredths of 2 times square root of x minus 3 sin x dx II: the integral from 0 to 48 hundredths of 3 sin x minus 2 times square root of x dx III: the integral from 0 to 1 and 386 thousandths of arc sin of quantity y over 3 close quantity minus y squared over 4 dy

I and III

Which is the area of the region in quadrant I bounded by y = 2x^2 and y = 2x^3? (1 point)

the integral from 0 to 1 of 2 times x squared minus 2 times x cubed dx

Express the area of the region bounded by the x-axis, y equals one half x minus 2 and y equals the cubed root of x comma using definite integrals. region bounded by x axis, y equals x to the one third power, and y equals one half x minus 2 highlighted on the coordinate plane

the integral from 0 to 4 of x to the power of one third dx plus the integral from 4 to 8 of x to the power of one third minus one half x plus 2 dx

Find the area of the region bounded by y = x2 + 2, y = x − 1, x = −2, and x = 2.

the integral from negative 2 to 2 of x squared plus 2 minus x plus 1 dx equals 52 over 3