mit_hacker said:I split the paths into two pieces. In the first one, x=t, y=t and we integrate from 0 to 1. However, for the second part, I am unable to come up with the parameterization. Please advise on how this is done.
mit_hacker said:Is it x=1 and y=t from 0 < t < 1??
Solving an integral with a bent line path involves finding the area under a curve that is not a straight line. This can be done by breaking the curve into smaller segments, using the trapezoidal rule, or by using the substitution method.
The trapezoidal rule is a method used to approximate the area under a curve by dividing it into trapezoids. This method can be helpful in solving an integral with a bent line path because it allows for the curve to be broken into smaller, more manageable segments.
Yes, the substitution method can be used to solve an integral with a bent line path. This method involves substituting a variable for a more complicated expression in the integrand, making the integral easier to solve.
Some tips for solving an integral with a bent line path include breaking the curve into smaller segments, using the trapezoidal rule, and using the substitution method. It can also be helpful to sketch the curve and visualize the area that needs to be calculated.
One common mistake to avoid when solving an integral with a bent line path is forgetting to divide the curve into smaller segments. Another mistake is using the wrong substitution or forgetting to substitute the variable back into the final answer. It is also important to check for any discontinuities in the curve that may affect the integral calculation.