
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
147. 

a) Find the area enclosed by the wave $ABC$ of the sine curve $y=\sin x\left(-\frac{\pi}{2} \leqslant x \leqslant \frac{3 \pi}{2}\right)$ and the line $A C$.

b) Find the area of the curvilinear triangle bounded by the sine curve $y=\sin x$, the x-axis, and the line $x=a$, where $a \leqslant \pi$.

148*. 

a) Find the area of the curvilinear trapezoid bounded by the $m$-th degree parabola $y=x^m$, where $m \neq -1$, the x-axis, and the lines $x=a$ and $x=b$.

b) Using the result from part (a), find the area of the curvilinear triangle bounded by the $m$-th degree parabola $y=x^m$ ($m > 0$), the x-axis, and the line $x=b$.

Present the answer in LaTex format: \boxed{Your answer}
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