Quick easy question -- quick way of integrating 9-x^2 (1 Viewer)

[blackops23]

Hi guys just wondering, is there any quicker way of integrating 9-x^2 without using the substitution x=3sinA??

Because part of a volumes question in my 4U trials involved integrating 9-x^2 --> And i used the substitution of x=3sinA, which resulted in a further 8 lines of working out.

However when I got back my paper, my teacher circled in red pen, the whole 8 line section of my working out for integrating 9-x^2 --> and sarcastically commented "Wow, you sure that's the way to do it?"

So yeah just wondering if there is a quick way to do integrate 9-x^2

Thanks guys

 

[slyhunter]

Integral is 9x-(x^3)/3+c?

 

[harrowed2]

9x-(x^3)/3+c

 

[AAEldar]

Hi guys just wondering, is there any quicker way of integrating 9-x^2 without using the substitution x=3sinA??

Because part of a volumes question in my 4U trials involved integrating 9-x^2 --> And i used the substitution of x=3sinA, which resulted in a further 8 lines of working out.

However when I got back my paper, my teacher circled in red pen, the whole 8 line section of my working out for integrating 9-x^2 --> and sarcastically commented "Wow, you sure that's the way to do it?"

So yeah just wondering if there is a quick way to do integrate 9-x^2

Thanks guys

Unless you mean:



In that case a trig substitution is the way to go for an indefinite integral.

HOWEVER, if it's a definite integral with boundaries then you can realise that the integral of that function is the area of a semi-circle so you can find it that way.

 

[Shadowdude]

Hi guys just wondering, is there any quicker way of integrating 9-x^2 without using the substitution x=3sinA??

Because part of a volumes question in my 4U trials involved integrating 9-x^2 --> And i used the substitution of x=3sinA, which resulted in a further 8 lines of working out.

However when I got back my paper, my teacher circled in red pen, the whole 8 line section of my working out for integrating 9-x^2 --> and sarcastically commented "Wow, you sure that's the way to do it?"

So yeah just wondering if there is a quick way to do integrate 9-x^2

Thanks guys

not sure if srs

 

[blackops23]

not sure if srs

shit, I meant root(9-x^2)

 

[AAEldar]

shit, I meant root(9-x^2)

In that case a trig substitution is the way to go for an indefinite integral.

HOWEVER, if it's a definite integral with boundaries then you can realise that the integral of that function is the area of a semi-circle so you can find it that way.

There.

 

[ohexploitable]

br8

 

[khfreakau]

br8

^