Consider the region between the graphs of f(x) = x2 and g(x) = 7x on [0, 7]. For the line of rotation given, use definite integrals to find the volume of the resulting solid. V= y 56 49 42 35 28 21 И 14 7 7 -7 -14 -21 -28 -35 -42 -49 -56 Around the line x = 8 2 4 6 10 12 14 16 X

Please solve and explain into details for me to understand. Thank you!

f(x, y) = x²ex² and let R be the triangle bounded by the lines x = 5, x = y/2, and y = x in the xy-plane. R (a) Express f f dA as a double integral in two different ways by filling in the values for the integrals below. (For one of these it will be necessary to write the double integral as a sum of two integrals, as indicated; for the other, it can be written as a single integral.) fRf dA = få fd f(x,y) d y where a = 0 d = 2x And f f dA = √₂ fª f(x, y) d R where a = , m = and q = , b = , b = d x 5 d n = + fm f f(x,y) d (b) Evaluate one of your integrals to find the value of ff dA. √ Rf dA = C = X " C = , p = d and d =