# Integration Limits: Is Upper Limit Always Greater Than Lower?

• Miraj Kayastha
In summary, integration limits are the boundaries of the independent variable(s) in a mathematical integration. The upper limit is always greater than the lower limit because it represents the end point of integration. The integration limits can be negative, and if the upper limit is smaller than the lower limit, the result will be negative. In some cases, the upper limit can be equal to the lower limit, resulting in an integral with a value of zero.
Miraj Kayastha
is the upper limit always greater than the lower limit in integration?

what should be the limits if we need to calculate total work done in bringing a mass from infinity to distance r from earth.

##\int_a^b f(x) \, dx = - \int_b^a f(x) \, dx##.

Miraj Kayastha said:
what should be the limits if we need to calculate total work done in bringing a mass from infinity to distance r from earth.

$\int$r

There is decrease in potential energy of system. So, negative work is done. -{infinity to r}

## 1. What are integration limits?

Integration limits are the values that define the boundaries of the independent variable(s) in a mathematical integration. They determine the range over which the function will be integrated.

## 2. Why is the upper limit always greater than the lower limit in integration?

This is because integration is a process of finding the area under a curve, and the upper limit represents the end point of the integration. It must always be greater than the lower limit, which represents the starting point.

## 3. Can the integration limits be negative?

Yes, integration limits can be negative. The limits simply define the range over which the function is integrated, and this range can include negative values.

## 4. What happens if the upper limit is smaller than the lower limit in integration?

If the upper limit is smaller than the lower limit, the integration will result in a negative value. This is because the integration is essentially finding the area under the curve in the opposite direction, which results in a negative value.

## 5. Are there any cases where the upper limit can be equal to the lower limit in integration?

Yes, there are cases where the upper limit can be equal to the lower limit. This typically occurs when the integrated function is equal to zero at both limits, resulting in an integral with a value of zero.

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