x & 0 & 3 & 6 & 9 & 12 & 15 f(x) & 0 & 2 & 6 & 12 & 20 & 30 The table above gives selected values for a continuous function f . If f is increasing over the closed interval [0,15] , which of the following could the value of int_(0)^15 f(x) d x ? A. 70 B 120 C. 160 D. 210

Given that is an increasing function over the interval , we can estimate the integral \(\int_{0}^{15} f(x) \, dx\) by considering the values of \( f(x) \) at the endpoints and midpoints of subintervals.Since is increasing, the value of the integral will be greater than the area under the curve formed by the minimum value of \( f(x) \) (which occurs at ) and less than the area under the curve formed by the maximum value of \( f(x) \) (which occurs at ).If we assume \( f(x) \) starts at a lower value and increases to a higher value, the integral should reflect this increase. Given the options:A. 70B. 120C. 160D. 210The most reasonable estimate for the integral \(\int_{0}^{15} f(x) \, dx\) given that is increasing would likely be around the middle range of the provided options. Therefore, the correct answer is:C. 160