Let and .If the area between the x-axis and the graph of in the closed interval is 0.115 where ,then what is the value of ? Round your answer to 3 decimal places.

Question

Let  ​ and  .If the area between the x-axis and the graph of  in the closed interval  is 0.115 where  ,then what is the value of  ? Round your answer to 3 decimal places. ​

Quizplus · Accepted Answer

The given problem involves finding the value of a definite integral. The integral represents the area between the x-axis and the graph of the function over a given interval. Using integration techniques, we can find the value of the integral and hence the answer.

The function 11eac44f_ee37_1874_bedf_23f3bbd12cbf_TB7497_11 can be represented as:

11eac44f_ee37_1874_bedf_23f3bbd12cbf_TB7497_11 = 11eac44f_ee37_1874_bedf_xc3_TB7497_11^3 - 3xc3 + 5

To find the integral of this function between the given limits, we can use the fundamental theorem of calculus or integration by substitution. Using either method, we get:

∫_11eac44f_ee37_3f85_bedf_e59a7f0e5281_TB7497_11^11eac44f_ee37_3f86_bedf_b727393cb193_TB7497_11▒〖11eac44f_ee37_1874_bedf_xc3_TB7497_11^3 - 3xc3 + 5 dx〗 = 8.205

Therefore, the answer is D.

Let ​ and

Let and