How to Change Integral Bounds
Learn to change the bounds of a definite integral to get the correct answer when doing calculus problems. A definite integral is a mathematical operation performed on an equation for a curve that results in the area under that curve. The bounds, also called limits, of the integral designate the range over which the computation is done. Frequently, to aid in solving a definite integral, a change in variable is performed. The bounds of the integral must also be changed accordingly, or the answer will be incorrect.
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Instructions
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Solve the change of variable equation for the new variable in terms of the old one algebraically. For example, a definite integral that once had a dependent variable "x" might be involved in the change of variable equation: u+2 = x, where "u" is the new variable. Solving for the new variable "u" leads to subtracting 2 from each side of the equation, or u = x-2.
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Substitute the old lower bound of the integral into the change of variable equation to get its new value. Assume the old lower bound was x = 0. Continuing the example, you have u = 0-2, or a new lower bound of u = -2.
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Substitute the old upper bound of the integral into the change of variable equation to get its new value. Assuming the old upper bound to be x = 10, you have u = 10-2, or a new upper bound of u = 8 for the integral.
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