Question

http://www.webassign.net/cgi-bin/symimage.cgi?expr=%20f%28x%29%20%3D%20%7B%28%207%20text%28%20for%20%29%20x%3C7%2C%20x%20text%28%20for%20%29%20x%3E%3D7%20%29%20

Answer 1

What do you have to do with that?

Answer 2

http://www.webassign.net/cgi-bin/symimage.cgi?expr=%20int_0%5E11%20f%28x%29dx%20

Answer 3

OK, in the case of piecewise functions we have to separate the integral in two integrals. Remember that the integral of a function can be thought as the area under the curve, so\[\int_a^b f(x) = \int_a^c f(x) + \int_c^b f(x)\](you cut the area in two pieces and then add them up).

Answer 4

Because of this,\[\int_0^{11} f(x) = \int_0^7 f(x) + \int_7^{11}f(x).\]I chose 7 because that's the point where the piecewise function changes from one function to the other. Between 0 and 7\[f(x) = 7\]and between 7 and 11\[f(x) = x\]so we get\[\int_0^{11} f(x)dx = \int_0^7 7dx + \int_7^{11} xdx.\]Does that make sense?

Answer 5

so its 11 correct?

Answer 6

As the final answer? No, 11 is not the answer. You have to find the antiderivative of 7 and the antiderivative of x and calculate both integrals separately.