Let be continuous on with on and on

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

q

be continuous on

[0,10]

with

q(x)\ge 0

[0,4]

and

q(x)\le 0

[4,10]

. The area under

q

above the

x

-axis on

[0,4]

9

square units. The areas between the graph of

q

and the

x

-axis on

[4,7]

and

[7,10]

are

6

and

k

square units respectively. Determine the value of

k

for which

\displaystyle\int_{0}^{10} q(x)\,dx=0