MAT 156 FINAL PROJECT 2In this project you will explain the formula NiMsKiIiIkYkKiZGJEYkIiIkISIiRicqJkYkRiQiIiZGJ0YkKiZGJEYkIiIoRidGJw==+...=NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI= . We define a sequence of definite integrals by the formula NiMvLUkiVEc2IjYjSSJuR0YmLUkkSW50R0YmNiQpLUkkdGFuR0YmNiNJInhHRiZGKC9GMDsiIiEqJkkjUGlHSSpwcm90ZWN0ZWRHRjYiIiIiIiUhIiI= .1. Calculate NiMtSSJURzYiNiMiIiE= and NiMtSSJURzYiNiMiIiI=. Use a substitution in NiMtSSJURzYiNiMiIiI= to show that it is equal to NiMqJi1JI2xuRzYiNiMiIiMiIiJGKCEiIg==. This part does not require numerical integration. Explain your answer and your choice of substitution.2. Calculate numerically NiMtSSJURzYiNiNJIm5HRiU= for NiMvSSJuRzYiIiIi, 2, ...10 and decide whether the sequence is increasing or decreasing. What is its limit? 3. Graph on the same graph the functions NiMpLUkkdGFuRzYiNiNJInhHRiZJIm5HRiY= for NiMvSSJuRzYiIiIi, 2, ..., 5 for in [0, NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=]. Which one is larger, which one is smaller? Why? What does this imply for the sequence NiMtSSJURzYiNiNJIm5HRiU= ?4. Show that NiMvLCYpLUkkdGFuRzYiNiNJInhHRihJIm5HRigiIiIpRiYsJkYrRiwiIiNGLEYsKiZGJUYsKiQtSSRzZWNHRihGKUYvRiw=. Which trigonometric identity do you use? Verify it for various NiNJIm5HNiI= using Maple.5. Use 4. to show that NiMvLCYtSSJURzYiNiNJIm5HRiciIiItRiY2IywmRilGKiIiI0YqRioqJkYqRiosJkYpRipGKkYqISIi . To do this you need to make a substitution in the integral NiMtSSRJbnRHNiI2JComKS1JJHRhbkdGJTYjSSJ4R0YlSSJuR0YlIiIiKiQtSSRzZWNHRiVGKyIiI0YuL0YsOyIiISomSSNQaUdJKnByb3RlY3RlZEdGOEYuIiIlISIi . Warning: Maple may not be able to calculate it for general NiNJIm5HNiI= . Parts 2 and 5 imply that NiMvLUkmbGltaXRHNiI2JC1JIlRHRiY2I0kibkdGJi9GK0kpaW5maW5pdHlHSSpwcm90ZWN0ZWRHRi4iIiE= . 6. Use NiMvLCYtSSJURzYiNiNJIm5HRiciIiItRiY2IywmRilGKiIiI0YqRioqJkYqRiosJkYpRipGKkYqISIi to show that: NiMtSSJURzYiNiMiIiU= =-(1-1/3-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=), NiMtSSJURzYiNiMiIic==(1-1/3+1/5-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=) ,etc. NiMtSSJURzYiNiMqJiIiIyIiIkkibkdGJUYp=+-(1-1/3+1/5-1/7+...-NiMqJkkjUGlHSSpwcm90ZWN0ZWRHRiUiIiIiIiUhIiI=). These results together with the limit from 5, show the formula required.7. Use the formula to calculate the first two decimal digits of NiNJI1BpR0kqcHJvdGVjdGVkR0Yk. How are you certain of the answer you provided? Hint: Alternating series.