The gallbladder is a small pouch that sits just under the liver. The gallbladder stores bile produced by the liver. After meals, the gallbladder is empty and flat, like a deflated balloon.efore a meal, the gallbladder may be full of bile and about the size of a small pear. In response to signals, the gallbladder squeezes stored bile into the small intestine through a series of tubes called ducts. Bile helps digest fats, but the gallbladder itself is not essential.
U-substitution is for functions that can be written as the product of another function and its derivative. $$\int u du$$. Integration by parts is for functions that can be written as the product of another function and a third function's derivative.
This has the eï¬ect of changing the variable and the integrand. When dealing with deï¬nite integrals, the limits of integration can also change. In this unit we. will meet several examples of integrals where it is appropriate to make a substitution.