# Sketch the bounded region enclosed by the given curves. Decide whether to integrate with respect...

## Question:

Sketch the bounded region enclosed by the given curves. Decide whether to integrate with respect to {eq}x {/eq} or {eq}y {/eq}. Draw a typical approximating rectangle and label its height and width.

{eq}y = 4x^2, \; y = 7x^2, \; 4x + y = 3, \; x \geq 0 {/eq}

Then find the area {eq}S {/eq} of the region.

## Finding the area using integration:

Integration has so many applications in real world scenarios. Integration can be used to find the area of the bounded region. The bounded region is found using graphs of the functions. Also, depending on the limits of integration, we can decide if we have to integrate the bounded region w.r.t. "x" or w.r.t. "y".

Below graph shows the various functions and the bounded region in yellow. Here we have to find the bounded region in yellow. Total area

S= (region 1)...

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