A. Given that  y = e^{√2x + 1} complete the table of values of y corresponding to x = 0.5, 1 and 1.5.B. Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate for the original integral, I, giving your answer to 4 significant figures.

C. Use the substitution t = √2X + 1 to show that I may be expressed as ∫^a_b kt e^t dt, giving the values of the constants a, b and k.

D. Use integration by parts to evaluate this integral, and hence find the value of I correct to 4 significant figures.

Transcribed Image Text:

X y 0 2.7183 0.5 1 1.5 2 2.5 9.3565 11.5824 3 14.0940