Question 1
Find the length of the curve y =
![](data:image/png;base64, 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)
x
2 -
![](data:image/png;base64, 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)
ln
![](data:image/png;base64, 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)
+7 from x = -2 to x = -1.
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![](data:image/png;base64, /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAAmABMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9D/iT4+1vwZ4v+H9haWlhJpXiHW10m4mmZ2nXNpdzkoowq4+zIMktne3yjaCcPxtf/FnS/FlrHpHiLwWlhqWpJb6fo1z4eup7trZVDTySXQv41UqiytkQkA7F+YsM6Xxf+GXin4ga/wCCL/QfE+kaBB4a1T+1zBqOhy37XM3kTQBd6XcARNlxJxtY7tpyACrdPYeDZoviDqfii+1I3xks47DTrPytiafDnfNg7jvaWQIWbA4hiXHykmtLRa3u7/h+ZU7OyXb8bv8AS3zOnoooqSTxTxR+y38KLDRp5dA+A/w31jVuFgtbzQ7K0gJ9ZJRbSMij1WNz/smsD4UfA34PfEDQtQl1b9n/AMAeHdb0vUZtL1CwTQbG6hWaPB3Qz/Z082NldGDFEPJBUEEV7F8ST4w/4RK6TwLb6TP4hkZUiOs3slrBGhPzuHSCY7wM7QYyucE5Awafwn0zX9F8LDT9f0HSNAmhlcxxaRrc2qibeS7zSzTWtu3mPIzs3ytkkndk4Dit3f8ArT+red+g5fCrb3/DX9fy8ztKKKKQgooooAKKKKAP/9k=)
- ln(2)
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![](data:image/png;base64, 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)
ln(2) -
![](data:image/png;base64, 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)
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![](data:image/png;base64, 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)
-
![](data:image/png;base64, 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)
ln(32)
◦
![](data:image/png;base64, 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)
+
![](data:image/png;base64, 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)
ln(2)
◦
![](data:image/png;base64, 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)
-
![](data:image/png;base64, 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)
ln(2)
Question 2
Find the length of the arc y = ln(sec x) between x = 0 and x =
![](data:image/png;base64, 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)
.
◦ ln(
![](data:image/png;base64, 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)
) units
◦ ln(1 +
![](data:image/png;base64, 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)
) units
◦ ln(2 +
![](data:image/png;base64, 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)
) units
◦ ln(
![](data:image/png;base64, /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAATABQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9U6+StSe112Hxn8Qdc0v4peJbafxFqlsuneDPFd/YwaLZabKdNY+VHqFskvmSWM10VijaUG5K7X2B29A8SeLr79mO21Lxv8RfFtxrfgS7hgOtakbdgui6gZGQTQ2qeY4tJhJbWwhjLtC0ETuJ2uLq5TB0uw8feCfgT8OfBD/DzxFrd5daDCPF99oN/pYuVvXiVr1S9xeQ75553neS4UuSWdwxd96p3fw7+e3z/r01Lgk37239befY988Hy6bceEtEl0a6mvtHexgayurm4luJZoDGvlu8spMkjFcEu5LMTliSSaKl8NyeboGnN/ZE2gD7OgGlT+TvtBgARHyXePKjj5GZeOCRRVySUmkZRvyrm3J9W0mx1/Sr3TNTsrfUdNvYXtrqzu4llhnidSrxujAhlZSQVIIIJBq3RRUlBRRRQB//2Q==)
- 1) units
◦ ln(2 -
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) units