A definite integral of the form Jate)as probably shouldn\'t be used O to approxi

Question

A definite integral of the form Jate)as probably shouldn't be used O to approximate ? b fok), where xkis some value in thek-th subinterval of [a,b] which is divided up Into. k-1 oto calculate the net change (from x- ato x- b) in a quantity whose rate of change with respect to x is given by fx). (loosely speaking) to accumulate "infinitely many quantities ).d" where Kx represents some physical quantity that is a function of x and dx represents infinitesimal changes in x (loosely speaking) to calculate "size in four-dimensional space-time" (defined to be an object's volume multiplied and x bthe ending time. O by its duration), by setting volume function), letting x represent time. X a represent the starting time, O to calculate power (defined to be work divided by tinel, by settingW(work function, letting xrepresent time, x- a represent the starting time, and x- b the ending time.

Explanation / Answer

Option (D) is correct.

When we talk about triple integrals we are working in the 3 dimensional space. And we are able to find the volume of the solid object.

But evaluating the definite integral of volume of a soild with respect to time time does not mean that by doing so we would get the size of the object.

And moreover, the remaining options are some of the applications of definite integrals.

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