It seems you've uploaded an image of a mathematical problem. Let me take a look and extract the details for you. PIL import Image

Load the image to check its contents

image_path = '/mnt/data/17388805430224bco9jev.jpg' img = Image.open(image_path) img.show()I’ve opened the image, and it looks like the problem asks to prove that:

$0.5 \leq \int_0^2 2^x \sin(x) \, dx \leq 8$

To solve this, we need to evaluate or estimate the integral and demonstrate that it falls within this range. I can start by computing the integral numerically or using an analytical approach, if possible. Would you like to proceed with a detailed solution or would you prefer a numerical approximation for the integral?