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# Warmup: Definite integral properties (no graph)

Apply the properties of definite integrals to evaluate definite integrals.

## Problem 1

Given integral, start subscript, minus, 5, end subscript, start superscript, minus, 1, end superscript, f, left parenthesis, x, right parenthesis, d, x, equals, 4, integral, start subscript, 3, end subscript, start superscript, 5, end superscript, f, left parenthesis, x, right parenthesis, d, x, equals, 9, and integral, start subscript, minus, 5, end subscript, start superscript, 5, end superscript, f, left parenthesis, x, right parenthesis, d, x, equals, 10, find the following:
a) integral, start subscript, minus, 1, end subscript, cubed, f, left parenthesis, x, right parenthesis, d, x, equals

b) integral, start subscript, minus, 1, end subscript, start superscript, 5, end superscript, f, left parenthesis, x, right parenthesis, d, x, equals

c) integral, start subscript, minus, 5, end subscript, start superscript, minus, 1, end superscript, 7, f, left parenthesis, x, right parenthesis, d, x, equals

d) integral, start subscript, 5, end subscript, start superscript, minus, 5, end superscript, f, left parenthesis, x, right parenthesis, d, x, equals

### Challenge

e*) integral, start subscript, 3, end subscript, start superscript, 5, end superscript, left parenthesis, f, left parenthesis, x, right parenthesis, plus, 4, right parenthesis, d, x, equals

## Problem 2

Given integral, start subscript, minus, 8, end subscript, start superscript, minus, 2, end superscript, g, left parenthesis, x, right parenthesis, d, x, equals, 11, integral, start subscript, minus, 8, end subscript, start superscript, 0, end superscript, g, left parenthesis, x, right parenthesis, d, x, equals, 5, and integral, start subscript, minus, 2, end subscript, start superscript, 8, end superscript, g, left parenthesis, x, right parenthesis, d, x, equals, minus, 5, find the following:
a) integral, start subscript, minus, 2, end subscript, start superscript, 0, end superscript, g, left parenthesis, x, right parenthesis, d, x, equals

b) integral, start subscript, 0, end subscript, start superscript, 8, end superscript, g, left parenthesis, x, right parenthesis, d, x, equals

c) integral, start subscript, 8, end subscript, start superscript, minus, 8, end superscript, 10, g, left parenthesis, x, right parenthesis, d, x, equals

### Challenge

d*) integral, start subscript, 0, end subscript, start superscript, 8, end superscript, left parenthesis, g, left parenthesis, x, right parenthesis, plus, x, right parenthesis, d, x, equals