MAT 156 FINAL PROJECT 3This project has two part.Part I. In this part you will compute the area of certain regions. Write here your social security number.Let NiNJImFHNiI= by the last digit of your social security number and NiNJImJHNiI= the one before.a:=b:=1. Define the functions NiMvLUkiZkc2IjYjSSJ4R0YmRig=, NiMvLUkiZ0c2IjYjSSJ4R0YmKiZGKCIiIiokLChGKEYqSSJhR0YmISIiRipGLiIiI0Yq, NiMvLUkiaEc2IjYjSSJ4R0YmKiRGKCIiIw==, NiMvLUkiY0c2IjYjSSJ4R0YmKiQsJkYoIiIiKiZJImJHRiZGKyIiIyEiIkYvRi4=. Plot the graphs of NiMtSSJmRzYiNiNJInhHRiU= and NiMtSSJnRzYiNiNJInhHRiU= on the same graph. Find the points of intersection. In the graph you should see two regions enclosed between the two graphs. Compute the areas of the two regions.2. Plot the graphs of NiMtSSJoRzYiNiNJInhHRiU= and NiMtSSJnRzYiNiNJInhHRiU= on the same graph. Find the points of intersection. In the graph you should see two regions enclosed between the two graphs. Compute the areas of the two regions.3. Plot the graphs of NiMtSSJnRzYiNiNJInhHRiU= and NiMtSSJjRzYiNiNJInhHRiU= on the same graph. Find the points of intersection. In the graph you should see two regions enclosed between the two graphs. Compute the areas of the two regions.4. Define the functions NiMvLUkjZzFHNiI2I0kieEdGJiomRigiIiIqJCwoRihGKkkiYUdGJiEiIiIiI0YuRi9GKg== and NiMvLUkjZzJHNiI2I0kieEdGJiomRigiIiIqJCwoRihGKkkiYUdGJiEiIiIiJEYuIiIjRio=. Plot on the same graph NiMtSSJmRzYiNiNJInhHRiU=, NiMtSSJnRzYiNiNJInhHRiU=, NiMtSSNnMUc2IjYjSSJ4R0Yl, NiMtSSNnMkc2IjYjSSJ4R0Yl. What do you notice concerning the points of intersection of NiMtSSJmRzYiNiNJInhHRiU= with each of NiMtSSJnRzYiNiNJInhHRiU=, NiMtSSNnMUc2IjYjSSJ4R0Yl and NiMtSSNnMkc2IjYjSSJ4R0Yl. Explain your answer.Part 2.5. Consider the Integral NiMtSSRJbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiYsJiIiIkYsKiYiIiNGLCokSSJ4R0YoRi5GLEYsRiwqJkYwIiImLCZGLEYsRi9GLCIiJCEiIkYw. Compute it directly with Maple. Now rewrite it as NiMtSSRJbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiYsJkkieEdGKCIiIiomIiIjRi0qJEYsIiIkRi1GLUYtKiQsJiokRiwiIiVGLSokRixGL0YtRjEhIiJGLA==. Explain why this is possible. This suggests the substitution NiMvSSJ1RzYiLCYqJEkieEdGJSIiJSIiIiokRigiIiNGKg==. Make this substitution with Maple and compute the integral. Do the two answers match? If they do not, reconcile them.
6. Consider the Integral NiMtSSRJbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiYsJiIiIkYsLUkjbG5HRiU2I0kieEdGKEYsRiwtSSVzcXJ0R0YlNiMsJkYsRiwqJComRjBGLEYtRiwiIiNGLEYsRjA=. Can Maple compute it directly? If not, guess the correct substitution that will allow Maple to solve it. Finally compute the integral.7. Compute the definite integral NiMtSSRJbnRHNiI2JComLCYiIiJGKS1JI2xuR0YlNiNJInhHRiVGKUYpLUklc3FydEdGJTYjLCZGKUYpKiQqJkYtRilGKkYpIiIjRilGKS9GLTtGKS1JJGV4cEdGJTYjRik=. Notice that for e we write exp(1). Compute it exactly based on your work in 6. and approximately using left-hand sums, right-hand sums, trapezoid and midpoint sums. Which ones are overestimates, which ones are underestimates and why?