Let F(x)=∫ sin(t^2) dt from 0 to x for 0≤x≤3. a) Use the Trapezoidal Rule with four equal subdivisions of the closed interval [0, 2] to approximate F(2). b) On what interval or intervals is F increasing? Justify your answer. c) If the average rate of change of F on the closed interval [0, 3] is k, find ∫ sin(t^2) dt from 0 to 3 in terms of k.

If the measure of angle 1 is 110 degrees and the measure of angle 3 is (2 x+10 degree), what is the value of x?

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling

Is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis.