Heat capacity of a gas
Heat capacity 
C_v
is the amount of heat required to raise the temperature of a given mass of gas with constant volume by 1°C, measured in units of cal/deg-mol (calories per degree gram molecular weight).
The heat capacity of oxygen depends on its temperature T and satisfies the formula
C_v = 8.27 + 10^(-5) * (26T − 1.87T²)
Use Simpson’s Rule to find the average value of C_v and the temperature at which it is attained for
20°C ≤ T ≤ 675°C.

Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.

∫ [cos(θ) / (sin²(θ) + sin(θ) − 6)] dθ

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

125. ∫ dx / (√x * √(1 + x))

Evaluate the integrals in Exercises 1–8 using integration by parts.

∫ x² sin(1 − x) dx

Evaluate the integrals in Exercises 33–36.

∫ [1 / √(9 - x²)] dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ (2 − cosx + sinx) / sin²x dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ t dt / √(9 − 4t²)