Evaluate the following integral using trigonometric substitution. Integral from 7 StartRoot 49 - x2 EndRoot dx
1. What substitution will be the most helpful for evaluating thisintegral?
2. Find dx?
3. Rewrite the given integral using substitution.

Step-by-step explanation:

1. Given the integral function , using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as i.e .

All integrals in the form are always evaluated using the substitute given where 'a' is any constant.

From the given integral, where a = 7 in this case.

The substitute will therefore be  

2.) Given

cross multiplying

3.) Rewriting the given integral using the substiution will result into;

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.