MAT - Paper 2011 - Q1G
Flashcards
Bounds of a transformed expression
If you know
\[-1 \le x \le 1\]
, what are the bounds for
\[a \le x^2 - 1 \le b\]
?
\[-1 \le x^2 - 1 \le 0\]
Shifting the variable inside an integral
How could you rewrite
\[\int^{b} _ {a} f(x-1) \text{d}x\]
?
\[\int^{b+1} _ {a+1} f(x) \text{d}x\]
How could you rewrite
\[\int^{b} _ {a} f(x+1) \text{d}x\]
?
\[\int^{b-1} _ {a-1} f(x) \text{d}x\]